Went on a site about special diamonds (9)
I believe the answer is:
persisted
'went on' is the definition.
(persisting is a kind of going on)
'a site about special diamonds' is the wordplay.
'a' becomes 'per'.
'about' is an insertion indicator.
'special' becomes 's' (common abbreviation as in Special Air Service**).
'diamonds' becomes 'd' (abbreviation in bridge say).
'site' enclosing 's' is 'siste'.
'per'+'siste'+'d'='PERSISTED'
(Other definitions for persisted that I've seen before include "Continued firmly or obstinately" , "Endured" , "Obstinately carried on" , "Kept going despite difficulties" , "Kept on against opposition" .)