Crossword Genius

Consume tea, perhaps, and a bit of supper (3,2)

Ross

I believe the answer is:

eat up

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

'consume' is the definition.
(I know that consume can be written as eat up)

'tea perhaps and a bit of supper' is the wordplay.
I cannot really see how this works, but
an anagram of 'tea' is 'eat' which is within the answer.
The remaining letters 'up' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for eat up that I've seen before include "show good appetite" , "Finish course" , "Finish one's food" , "polish off" , "43 [TUCK] in" .)

I've seen this clue in the Evening Standard.
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