Green’s Dictionary of Slang

shove, the n.

[late 19C+] dismissal from one’s employment.

In phrases

get the shove (v.)

1. [late 19C+] to be dismissed from a job.

2. [1900s] to be rejected by a lover.

3. [2000s] in sports contexts, to be dismissed from the game.

give someone the shove (v.) (also give the shove to someone)

[late 19C+] to dismiss, usu. from a job.