Mind, or keep an eye on, later (4,5)

I believe the answer is:

look after

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'mind' is the definition.
(I've seen this before)

'keep an eye on later' is the wordplay.
'keep an eye on' becomes 'look' (I can't justify this - if you can you should give a lot more credence to this answer).
'later' becomes 'after' (I've seen this before).
'look'+'after'='LOOK AFTER'

'or' acts as a link.

Can you help me to learn more?

(Other definitions for look after that I've seen before include "mind" , "Take care of" , "Tend" , "Watch over" , "Supervise" .)

I've seen this clue in the Evening Standard.

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