Drinks cuppa, left unfinished in hurry (5)
I believe the answer is:
haste
'hurry' is the definition.
(haste is hurrying or rushing)
'drinks cuppa left unfinished' is the wordplay.
'drinks' becomes 'has' (I can't justify this - if you can you should give a lot more credence to this answer).
'cuppa' becomes 'tea' (informal term for a cup of tea).
'left unfinished' means to remove the last letter.
'tea' with its last letter removed is 'te'.
'has'+'te'='HASTE'
'in' acts as a link.
Can you help me to learn more?
(Other definitions for haste that I've seen before include "''Marry in . . . . ., repent at leisure''" , "Expedition" , "dispatch" , "Rash speed" , "go at speed" .)