It's been a while since I read the books but I feel that The Expanse TV Series has drastically changed in regards to Drummer's storyline.
From what I remember in the 5th book of The Expanse series (Nemesis Games):
This is the first time she appears in the series and she is a part of Fred Johnson's crew on Tycho. She is an important person within the crew on Tycho, but doesn't really become a central character until the 7th book, Persepolis Rising.
Maybe on a sub-question, why has Drummer's story differed from the books in the TV Series?