【give someone a push】 —

1. shove a person:

• Just at the edge of the well, he gave him a push and threw him into it.

2. said of an act of pushing smb.’s car:

• Our car was stuck and they gave us a push.

3. (coll.) promote smb.’s advancement; assist a person:

• I was including his business on my newsletters just to give him a push.

4. (sl.) dismiss a person from employment:

• I just recall a few months ago when it looked like they were going to give him a push.

【give someone the push】 — = 【give someone a push】 4:

• If he doesn’t resign after this term—which he won’t—we’ll just have to give him the push.