Delay the man's opening of international gallery? (8)
I believe the answer is:
hesitate
'delay' is the definition.
(hesitating is a kind of delaying)
'the man's opening of international gallery?' is the wordplay.
'the man' becomes 'hes' (I've seen this in other clues).
'opening of' suggests taking the first letters.
'gallery?' becomes 'tate' (Tate Modern, Tate Britain etc).
The initial letter of 'international' is 'i'.
'hes'+'i'+'tate'='HESITATE'
(Other definitions for hesitate that I've seen before include "Dither indecisively" , "Hold back in doubt" , "Pause, waver" , "Lack confidence" , "Stall" .)