郵便局に行って

go to the post office

→ 郵便局
phrase Rare #30,869
go to the post office 行って is the te-form of 行く (to go), often used to connect this action to what comes next. In 郵便局に行ってきた, it means someone went to the post office and came back.
JA: 郵便局に行って、切手を買います。
EN: I’ll go to the post office and buy stamps.

郵便局に行って、新しい郵便番号が何番か聞いてきて。

Go to the post office and ask what the new ZIP code is.

切手を買いに郵便局に行ってきた。

I went to the post office to buy stamps.