keep on phrasal verb (see also keep)

1. to continue doing something, or to do something many times
keep on doing something
You just have to keep on trying.

2. keep somebody ↔ on to continue to employ someone, especially for longer than you had planned:
If you’re good, they might keep you on after Christmas.

3. British English informal to talk continuously about something or repeat something many times, in a way that is annoying Synonym : go on
keep on about
There’s no need to keep on and on about it!
keep on at
If I didn’t keep on at the children, they’d never do their homework.

[TahlilGaran] Dictionary of Contemporary English ▲

keep on
1. • keep (someone) on
allow someone to continue working for you
Although we have too many workers we have decided to keep everybody on until business improves.

2. • keep on (doing something)
continue
She is careless and keeps on making the same mistakes over and over.

[TahlilGaran] English Idioms Dictionary ▲

keep on
v.
1. To go ahead; not stop; continue.
The neighbors asked them to stop making noise, but they kept right on.
Columbus kept on until he saw land.
■ Often used before a present participle.
Relentlessly, the boy kept on asking about the birds and the bees.
The boy kept on talking even though the teacher had asked him to stop.
Synonym: GO ON.
Compare: KEEP AT, KEEP UP.
2. To allow to continue working for you.
The new owner kept Fred on as gardener.

[TahlilGaran] English Idioms Dictionary ▲

keep someone on
• keep (someone) on
allow someone to continue working for you
Although we have too many workers we have decided to keep everybody on until business improves.

[TahlilGaran] English Idioms Dictionary ▲