Crossword Genius

Has tea, but can't finish it in the rush (5)

Ross

I believe the answer is:

haste

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

'the rush' is the definition.
('haste' can be a synonym of 'rush')

'has tea but can't finish it' is the wordplay.
I cannot quite understand how this works, but
'tea' could be 't' (I've seen this in other clues) and 't' is located in the answer.
'it' could be 'e' ('e' can mean 'electronic' which is similar to 'IT') and 'e' is found in the answer.
The remaining letters 'has' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'in' is the link.

Can you help me to learn more?

(Other definitions for haste that I've seen before include "Undue speed" , "Expedition" , "Rush; urgency" , "Expeditiousness" , "make speed" .)

I've seen this clue in the Evening Standard.
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