expression, ichidan verb
inform in advance; give notice; ask permission beforehand
Used when you notify someone or seek their consent before taking an action. Often implies politeness or consideration. The cross-reference to 断る (sense 2) suggests a connection to declining or giving notice, but here the focus is on prior notification or asking permission.
See also: 断る
会議を欠席するときは、事前に上司に断りを入れてください。
When you will be absent from a meeting, please inform your boss in advance.
彼は隣の家に断りを入れてから木を切った。
He cut the tree after asking permission from the neighbor.