I've gotta come here every year.

Literal

Every-year here [to-に] come-have-to-[contracted-なきゃ].

来なきゃ is a contracted form of 来なければ (ならない/いけない) — casual spoken Japanese drops the ならない and shortens the conditional. なきゃ alone implies 'must X' without saying the whole thing. Very common in casual conversation.