Cuckoo nest he reveals with no adult yet (12)
I believe the answer is:
nevertheless
'yet' is the definition.
(I know that yet can be written as nevertheless)
'cuckoo nest he reveals with no adult' is the wordplay.
'cuckoo' is an anagram indicator (I've seen this in other clues).
'with no' is a deletion indicator.
'adult' becomes 'a' (abbreviation).
'nest'+'he'+'reveals'='nesthereveals'
'nesthereveals' with 'a' removed is 'nestherevels'.
'nestherevels' anagrammed gives 'NEVERTHELESS'.
(Other definitions for nevertheless that I've seen before include "anyhow" , "In spite of everything" , "at any rate" , "Notwithstanding" , "But always" .)