Stop meeting and give something (not everything) away? (4,5)

I believe the answer is:

keep apart

I'm a little stuck... Click here to teach me more about this clue!

'stop meeting and give something' is the definition.
I can't judge whether this defines the answer.

'everything away?' is the wordplay.
'everything' becomes 'keep' (I am not sure about this - if you are sure you should believe this answer much more).
'away?' becomes 'apart' (I've seen this in another clue).
'keep'+'apart'='KEEP APART'

'not' is the link.

Can you help me to learn more?

I've seen this clue in The Times.

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