Right now, the only other review of this card is almost 5 years old.
In the meantime, the fourth, fifth, sixth and seventh rotation happened.
Belonging to Downfall, Divested Trust is now among the oldest cards in the whole standard format.
After more than 6 years in the active cardpool this agenda has seen … not much actually.

Let's revisit Divested Trust in the light of what's basically a different game now than 6 years ago.
Let's revisit Divested Trust in the light of Elevation and, more specifically, BANGUN: When Disaster Strikes.

I wrote a silly story of me using it in the form of a decklist, but for the sake of an actual review I'll go more into the mechanics.  

Scoring  a 3/1 is always a pain.
You have the same effort as scoring a solid 3/2 agenda, but you only get 1 point and in the special case of this one you don't even get to keep that point, since the whole point of  Divested Trust is to be forfeited.
And not in a good way (like the newest agenda that wants to be forfeited) that enables other cards. No, Divested Trust's sole purpose lies in an ability that requires forfeiting itself as a cost.

This is a lot to ask. The fact that the pace of the game generally is faster now than it was when Divested Trust was made actually makes this even more of a burden.

But it gets worse:
Divested Trust wants to be scored early, so that it can still be used when the runner steals an agenda without immediately winning the game. 
This makes it hard to use in any environment where the runner can get to 4 points reasonably fast. 
Bad news, that's the only environment we have. Corps can't really have a safe early game against the modern arsenal of early aggression tools on the runner side.

And there's another downside: 
Divested Trust wants to be scored early, but without really doing that much to help the corp to develop.
Other 3/1s either accelerate the game instantly or continue to provide some sort of meaningful protection. 
Divested Trust does both once at some future point in the game barely under your control as a corp player.

The one silver lining for this card is that it's super fun (for the corp) and swingy when it actually does "un-steal" (a very rare mechanic) 2 or 3 points the runner fought hard for, while simultaneously re-funding a corp that has spent a lot to defend these points. 
These moments are the reason I like the design concept, even if the card isn't objectively good.

Conclusion

In their early days of keeping this game alive NSG erred on the side of caution with this cool and unique agenda.
It's not good.
You should play it more often.

After a long list of fixed strength breakers (including Cleaver, Buzzsaw and Mimic in the current rotation), we now get a fixed strength breaker. This alone makes Umbrella an exceptional program. So let's look at what we've got here ...

Typically, fixed strength breakers need a way to meet the strength requirements of big ICE by either getting strength support (the way) or reducing the ICE strength (the way).
So what ICE exactly do we need to deal with? Let's start an NRDB search for Code Gates with more strength than Umbrealla ... Oh, what a suprisingly short list! Let's filter it for rotation ... And we found Valentão. That's it. Only one (in numbers: 1) Code Gate in the game that's out of strength reach and it's arguably a rather niche ICE that won't be found in most Corp decks, unlike the rotated Macrophage or DNA Tracker. And we don't even have "growing" Code Gates like we have with some Barriers that can get more and more strength over the course of the game.

So, basically, we have a fixed strength breaker with simply enough strength. Not 3 strength and you cover the rest, but just enough strength.
Now we can go and break any Code Gate for just 2, right?
Well, there's another catch. With strength out of the way as a requirement we have a breaker that can break any Code Gate that hosts a Trojan, no matter what.
This means, instead of a breaker that needs support for high strength ICE we have a brekaer that needs support in the form of 1 Trojan per Code Gate.
That's potentially a lot of you might need if the Corp is running a lot of Code Gates.

When we check the list of all Trojans in the current rotation we find 14 programs, half of them in faction with Umbrella. Quite a list.
We have Hush for Tollbooth, obviously.
We have newcomers like Pichação that are designed with a whole Trojan based runner archetype in mind ("Hello, Arissana, nice to meet you.").
We finally get to see the sleeper card Kyuban back from 5 years ago shine.
And I'm pretty convinced that the second half of the Liberation cycle will only bring us more Trojans.

So, yes, really an exceptional new Icebreaker we got here. One that really feels different.

This card is weak, because it is designed with crippling limitations.

Usage

On first sight, the effect is super strong.

• It can get you through a lot of ICE cheaply. If it has only a single ETR, you can pass it. No matter the strength.
  Is that 5+ str barrier taxing you? "Break" for 1.
  Is the enemy trying to rush behind some cheap gear check ICE? Break any of the list with one card.
• It counters one-time ETR effects like Nisei MK II, Border Control and Bio Vault.
  This is huge! Robbing the Corp one of their Nisei counters can easily win a game.

Limitations

This is where it gets ugly.

• "Use this ability only if you made a successful run on HQ this turn." is the main showstopper.
  If this would instead read "Install Lucky Charm only if you made a successful run on HQ this turn." the card would be actually usable.
  This basically adds the cost of running HQ on top of the card costs and, even worse, makes the card useless on HQ runs, aka the runs where it would be most useful for in faction.
• The "Remove this hardware from the game" part is both a deliberate lack of synergy with Geist and The Back and the reason why this card can't keep doing it's job.
  The Corp player can recur his Border Control with Preemptive Action, but you can only defend against it once with Luck Charm.
  Circumventing this by slotting 3 copes is just ridiculous, since it won't be useful in a lot of matchups.
• The fact that this is a ♦ card is probably important for balancing reasons.
  Specifically, for the same reasons that you can't have multiple Boomerangs out.
  Still, it is a limitation, since this can't get you though multiple ETR ICE or multisub ETR ICE.

Related Cards

This is basically another limitation of LC: The alternatives and lack of synergy.

• As already mentioned, it has no synergy with The Back, which is a huge letdown for Az and Geist, the main IDs that would want to use it.
  Az can still install LC for free, which is always nice, but far from enough to make it viable for him.
  Apex could make use LC, since he mostly cares about getting through and way less about hurtful s than most other runners. But paying 2 influence for this card? Not really gonna happen.
• Boomerang does the job of "get me through this ICE once" way better. It has it's own limitations, but they are by far outweighed by the self-recurrence.
  Heck, the lack of a "remove from game" alone would make Boomerang better.
  That, and the protection against nasty non-ETR subs.
• Jak Sinclair is so non-existing in the meta that he is barely worth mentioning here, but I still do it, because of another deliberate lack of synergy.
  As a hardware that can make runs successful, Jak would love this, if it wasn't for the need of running HQ first, which completely kills any synergy between these two cards.

TL;DR

Bad card.

List of runner cards that cost at least 7 to install.

I mostly agree with @BlackCherries. And I mainly posted this review to fix the link.
But I wouldn't write off the Nexus so easily. It has been a thing in criminal and might get a comeback.

Plus, installing a Shard without the run might be situational good. Not reason enough to put either shards or Kiting into a deck that wouldn't need it without the other, but still handy occasionally.

EDIT: Link fixed.

From the UFAQ:

If the Runner uses Fall Guy to prevent Bug Out Bag from trashing itself, do they still draw cards?

Yes. Trashing Bug Out Bag is part of the effect of the ability not a cost or condition.

So, let me get this straight... Nothing on the card says anything about removing counters. So if you prevent the trash, you can just keep it and use it again. You could load it with, like, 7+ counters, and use it alongside 3 Fall Guys as a janky semi-permanent draw engine. Load it once and you can end 4 turns with no cards in hand to draw 7+ cards and be good for the next turn or two. That's a lot of draw. Enough, actually, to draw most of your deck and be considered your main draw engine.
As long as your deck has a consistent way of getting rid of spare cards before the end of the turn, like for example Faust, Bookmark, Severnius Stim Implant, The Noble Path or maybe some self-damage tricks.

Another interesting synergy is Safety First.
At the end of the turn, it's checked if your grip is empty. If it is, both Safety and BOB trigger simultaneously. The runner simply chooses to resolve Safety first (pun intended), gaining 1 card and then still gaining X cards from BOB despite his hand not being empty anymore, because it was empty when the end-of-turn triggered. So the runner ends up with X+1 cards in grip.
That might actually do some good work in an Adam deck that burns cards fast.