What Genesis? Khan killed everyone who worked on it except for Drs. Marcus and Marcus then blew it up together with himself the ship and most importantly the computer. Kruge destroyed the scence vessel which was studying the planet. and killed David Marcus.
Kruge died. Valkris died. Torg died.
That leaves Carol as the only person knowledgeable about it. And even if she tried to re-develop it, without David's secret -- protomatter -- it probably wouldnt work at all.
(it would depend on Saavik to tell about it --or Maltz! he survived!--, but I dont think she would. She must hate Genesis. She didnt like prtomatter BEFORE she lost her BF and got knocked by a zombie because of it.
There is no more Genesis for anyone.