Drink a quart and careen, half-cut: who'll worry? (5,5)
I believe the answer is:
drama queen
'who'll worry?' is the definition.
'drink a quart and careen half-cut' is the wordplay.
'drink' becomes 'dram' (small alcoholic drink).
'quart' becomes 'qu'.
'and' means one lot of letters go next to another.
'half cut' means to take half the letters.
'careen' with half the letters taken is 'een'.
'dram'+'a'+'qu'+'een'='DRAMA QUEEN'
(Other definitions for drama queen that I've seen before include "One prone to histrionics" , "one excited often" , "Male or female prone to histrionics" , "Gertrude, perhaps" , "woman prone to histrionics" .)