I don't know that anybody gets better over time in literature

Maybe Thomas Hardy, though assessing that is complicated by the fact that he basically switched completely from novels to poems partway through his career and it's not clear how you compare the quality of such different forms.

Maybe Shakespeare; looking at a chronological list of his plays I certainly see a higher density of ones I know to be good later on. (But Shakespearean chronology is uncertain and I'm not familiar with all his plays.)

Jane Austen, kinda; the novels for which she's famous were written in the last six years of her life. (But, tragically, all Austen's works are early works; she died at 41.)

Dostoyevsky's first published work was in 1846 (when he was 25). The earliest "big name" one would be "Notes from Underground", 1864, age 43, more than half-way through his writing career (his last novel was "The Brothers Karamazov" from 1879).

Goethe was already something of a big name at 25, but his best novel is probably Wilhelm Meister (age 46) and his best play Faust part 1 (age 59).

I dunno; it looks to me as if writers get better, get worse, stay about the same, or evolve their style in ways that make comparison difficult, and all of those happen pretty often.