Pepper for one’s cooking gran set close to stove (8)
I believe the answer is:
sergeant
'pepper for one's' is the definition.
(Sergeant Pepper, character in a Beatles song)
'cooking gran set close to stove' is the wordplay.
'cooking' indicates anagramming the letters (cook can mean to falsify or distort).
'close to' indicates one should take the final letters (the 'close' to the word).
The last letter of 'stove' is 'e'.
'gran'+'set'+'e'='gransete'
'gransete' with letters rearranged gives 'SERGEANT'.
(Other definitions for sergeant that I've seen before include "Noncommissioned military officer" , "one with stripes" , "CARRY ON FILM" , "NCO; Death a fell one, Hamlet" , "Military rank" .)