Scrap, initially overlooked, vet gives for recycling (7)
I believe the answer is:
vestige
'scrap' is the definition.
(thesaurus)
'initially overlooked vet gives for recycling' is the wordplay.
'initially overlooked' means to remove the first letter.
'for recycling' is an anagram indicator.
'vet'+'gives'='vetgives'
'vetgives' with its first letter removed is 'etgives'.
'etgives' with letters rearranged gives 'VESTIGE'.
(Other definitions for vestige that I've seen before include "2 [HINT]" , "Small trace" , "'Shadow, trace (7)'" , "Slight amount, hint" , "(Last) trace" .)