Stubborn old boys at home in gallery (9)
I believe the answer is:
obstinate
'stubborn' is the definition.
('obstinate' can be a synonym of 'stubborn')
'old boys at home in gallery' is the wordplay.
'old boys' becomes 'obs' (I've seen this in other clues).
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'in' is an insertion indicator.
'gallery' becomes 'tate' (I've seen this before).
'in' inserted inside 'tate' is 'tinate'.
'obs'+'tinate'='OBSTINATE'
(Other definitions for obstinate that I've seen before include "Stubborn or unyielding" , "Blindly stubborn" , "Cussed" , "Like mules" , "headstrong" .)