'Offspring' providing accompaniment around finale (10)
I believe the answer is:
descendant
'offspring' is the definition.
(thesaurus)
'accompaniment around finale' is the wordplay.
'accompaniment' becomes 'descant' (descant is a kind of accompaniment).
'around' is an insertion indicator.
'finale' becomes 'end' (I've seen this before).
'descant' enclosing 'end' is 'DESCENDANT'.
'providing' acts as a link.
(Other definitions for descendant that I've seen before include "Later family member" , "Progeny" , "One from a long line" , "Grandson maybe" , "Future person in one's family line" .)