Carol happy when drunk? That’s not true (10)
I believe the answer is:
apocryphal
'not true' is the definition.
(apocryphal can mean dubious or made-up)
'carol happy when drunk?' is the wordplay.
'when drunk?' indicates anagramming the letters (I've seen this in other clues).
'carol'+'happy'='carolhappy'
'carolhappy' is an anagram of 'APOCRYPHAL'.
'that's' is the link.
(Other definitions for apocryphal that I've seen before include "Fabulous" , "probably made-up" .)