Well all right then

Essentially, the way I see things is Beria was heavily invested and depended on Uncle Joe himself. AFAIK most the Politburo detested Beria personally so once Stalin kicks it things look grim for Beria, as OTL proved
Now, in terms of how he actually might become the leader, to be honest I'm pretty fuzzy as to have that actually occur. Now, per your OP, killing Khrushchev, mmm I don't think that will do it, as like I said it still won't stop someone else filling the void and simply dispensing Beria since aside the The Boss his power base was quite limited, and push come to shove Zhukov wouldn't support Beria neither would IMO the Politburo.
Also going back to Khrushchev, AFAIK it was actually a couple of years after Stalin's death that he came to the forefront of leadership, so, that is something to think about I guess. One thing is really interesting though; From what I've read Beria actually was as pro-west as a Soviet could get away with, so let have some fun *handwave* Zhukov, Kruschev, Molotov et all suffer Collective Heart Attacks (no Pun intended...okay maybe a little) Beria pick up the pieces, maybe institues a more peaceful co-existance policy? All pure speculation on my part mind. Cheers