手を打って

take action; settle for

→ 手
phrase Rare #33,363
take action; settle for 手を打つ can mean taking measures to deal with a situation, often proactively. In negotiations, it can mean accepting or settling for a particular offer. The て-form 手を打って connects it to what follows.
JA: 問題が大きくなる前に、何か手を打っておこう。
EN: Let's take action before the problem gets worse.

まで忘れないように手を打ってやる

I'll teach you a lesson so you won't forget next time.

— さらば、わが愛/覇王別姫 (1993)

何か手を打っておくべきだった

I should have done something about it.

彼らが早く釈放されるように手を打っていただきたい

I would like you to take steps to ensure that they are released as soon as possible.

ケーキ一個手を打ってあげるよ

I'll settle for one cake.