Richard Dawkins suggested (tongue somewhat in cheek) that we could extend average human life span by only allowing people over a certain age (say 35) to breed. On average, only people who do not carry genes apt to prove lethal in early middle age would have kids. The next generation would not be allowed to breed before forty, and so on. Eventually you would have a breeding population (probably via a narrow population bottleneck) of people purged of early and mid life lethal genetic variants, who were fertile into their later years. No biotech required.
Nb. I'm paraphrasing and taking what he said out of context. He was not proposing the idea, just discussing an implicaion of genetic theory.
I believe the experiment has been tried with fruit flies and has resulted in major lifespan lengthening, but I can't see it catching on with humans.