Stops rushing and has a leisurely drink? (5,2)

I believe the answer is:

slows up

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'stops rushing and' is the definition.
I can't judge whether this defines the answer.

'a leisurely drink?' is the wordplay.
'a leisurely' becomes 'slow' (I've seen this before).
'drink?' becomes 'sup' (to sup is to drink).
'slow'+'sup'='SLOWS UP'

'has' is the link.

Can you help me to learn more?

I've seen this clue in the Evening Standard.

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