You unlock the Needle upgrade in Hollow Knight: Silksong by speaking to Pinmaster Plinney in Bellhart. It's as simple as that, but the path to get to this point is difficult because you need to defeat two strong bosses almost back-to-back.
Bellhart is the haunted city you find right after defeating Moorwing in Greymoor. If you have no idea what I'm talking about, bad news: You're too far from the Needle upgrade and should wait until you defeat Moorwing, which is the fifth boss in Silksong and the one that follows Fourth Chorus.
