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Wiktionary
get on with

vb. 1 (context transitive English) To proceed with; to begin or continue, especially after an interruption. 2 (context transitive English) To have a good relationship with.

WordNet
get on with

v. have smooth relations; "My boss and I get along very well" [syn: get along with, get on, get along]

Usage examples of "get on with".

As far as Reynaud had been able to tell, Young was simply incapable of watching someone else get on with his job in an orderly fashion as long as he could interfere without exerting himself.

Anything else was a matter for the Navy to deal with, and some of the interest in his eyes faded as he waited for them to get on with it.

This time there was no secret reserve in his mind, no promise that after this he would get on with his journey to Mizzer.