Angry about finishing late, you need a drink (4)
I believe the answer is:
mead
'a drink' is the definition.
(mead is a kind of drink)
'angry about finishing late' is the wordplay.
'angry' becomes 'mad' (similar in meaning).
'about' means one lot of letters goes inside another.
'finishing' indicates one should take the final letters (the letter which finishes the word).
The final letter of 'late' is 'e'.
'mad' enclosing 'e' is 'MEAD'.
'you need' acts as a link.
(Other definitions for mead that I've seen before include "Honey drink; lea" , "Cooked joint" , "something to drink" , "Honeyed drink for dame" , "Alcoholic drink of fermented honey and water of old" .)