Peculiar to a big lob, it’s essential to the score (9)
I believe the answer is:
obbligato
'essential to the score' is the definition.
(musical term describing an essential instrument)
'peculiar to a big lob' is the wordplay.
'peculiar' indicates anagramming the letters (a peculiar or strange ordering of the letters).
'to'+'a'+'big'+'lob'='toabiglob'
'toabiglob' is an anagram of 'OBBLIGATO'.
'it's' is the link.
(Other definitions for obbligato that I've seen before include "a must for the player" , "Musical part not to be omitted" , "Has to be done" , "Instrumental part integral to a piece of music - I go to blab (anag)" , "Essential part of a music score" .)