Fetching details from the dictionary...

bureau; department
office (e.g. post, telephone); broadcasting station (e.g. television, radio); channel; exchange
affair; situation
game (of go, shogi, etc.)
「局」 has another reading with different meanings.
税務局に届け出を出した。
I filed a report with the tax bureau.
郵便局で荷物を送ってきたよ。
I sent a package at the post office.
局面が変わってきたと感じるよ。
I feel the situation is changing.