Excite object? I will, in gallery (9)
I believe the answer is:
titillate
'excite' is the definition.
(I know that titillate is a more specific form of excite)
'object? i will in gallery' is the wordplay.
'object?' becomes 'ti' (Ti is an example).
'i will' becomes 'I'll' (abbreviation).
'in' indicates putting letters inside.
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'ill' going within 'tate' is 'tillate'.
'ti'+'tillate'='TITILLATE'
(Other definitions for titillate that I've seen before include "Interest superficially" , "Arouse mildly (with images)" , "Tease" , "Excite pleasurably" , "Stimulate agreeably" .)