Consumes tea, perhaps, before starting supper (4,2)

I believe the answer is:

eats up

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

'consumes' is the definition.
(I've seen this in another clue)

'tea perhaps before starting supper' is the wordplay.
I cannot really see how this works, but
an anagram of 'tea' is 'eat' which is present in the answer.
The remaining letters 'sup' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in the Evening Standard.

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