Core fabric is deep (9)
I believe the answer is:
heartfelt
'is deep' is the definition.
(thesaurus)
'core fabric' is the wordplay.
'core' becomes 'heart' (synonyms).
'fabric' becomes 'felt' (felt is a kind of fabric).
'heart'+'felt'='HEARTFELT'
(Other definitions for heartfelt that I've seen before include "Sincerely intended with strong feeling" , "With sincere passion" , "unfeigned sincerity" , "Deeply sincere" , "Most fervent in cardiac way" .)