This card is getting some love in the reviews so far. I really hope the positive reviews are right - heck, I argued in favour of Fisk Investment Seminar on this very site. I want cards to be playable and powerful and fun. Here though, I'm going to play devil's advocate. My suspicion is that in the final analysis this card sucks.
Compare this to Archived Memories from a purely economic perspective. They both take a to play. With Archived Memories that's the end of the story. You've recurred a card that you want in your hand. By contrast, Allele repression needs advancing before it does anything. 1 and a for each card you want back. Then you have to rez it for a cost of 2. Then you have to spend another card for each card you want to recur. That's some expensive recursion. Sometimes the extra cards you discard will be stuff you don't need: silver bullets that aren't appropriate to the match-up, ice that doesn't help your current board-state, Shocks and the like. That's not going to happen reliably though. I don't know about anyone else, but I'm not in the habit of putting cards that I consider 'junk' in my deck.
All this expense might be justified if Allele Repression was the key to combotastic awesomeness, and it's clear that a lot of folks think that it is. The card most often mentioned is Snare!, and I think that's the best argument for repressing alleles. I'll come back to it. Other candidates mentioned by Bigguyforyou are Neural EMP and Trick of Light. With the former, Ronin instead of Allele Repression does the same job better. Allele Repression offers more versatility, but it will never be king of the kill. The latter could be helpful sometimes, but you need an awful lot of advanced things on the table to make that work. If your deck advances things and then Tricks out agendas it's already quite complicated. More moving bits increases the need for your deck to come out in a particular order and put pressure on slots that you'd really like to fill with ice and economy.
At this point I should talk about Mushin No Shin. With Mushin you can circumvent the cost of playing Allele Repression and with Allele Repression you can recur Mushin. It's a match made in heaven! Except no. Mushin is in many ways an economy card, so saying it makes Allele Repression playable is like saying Hedge Fund makes Clairvoyant Monitor playable. There are already quite a lot of good targets for Mushin. The opportunity cost for a Mushined Allele Repression is a Mushined much-better-card. On the other hand, if you're recurring Mushin with Allele Repression then your strategy is eating itself. I'm going to install and advance a card in order to recur (with some additional expense) a card which provides economy with which to install and advance cards! It can't possibly go wrong.
So. Snare. I can imagine the situation where a runner plays Legwork. In the paid ability window after the runner has committed to access I pop my Allele Repression (which I'm imagining I mushined more than a turn ago and further imagining the runner chose not to run) and fill my hand with three Snare!s. I imagine the requisite Snare!s are already in my archives after a long hard fought game. At this point I imagine the runner's legwork will hit two or more of the Snare!s. The odds are in favour of such an outcome given the circumstances. I'm also imagining that the runner hasn't siphoned me broke because I'm Jinteki and that's what happens to Jinteki if it doesn't spend its precious utility slots on Caprice Nisei instead of Allele Repression. In this situation that I'm imagining Allele repression would win me the game. I'm sure it will happen sometimes, but probably not often enough.
One last criticism. It's a 2 to trash, so on top of everything else, it makes R and D porous. Like I say, I'd love to be wrong, but the bottom line for me is that the expense and opportunity cost just aren't going to justify themselves often enough.