Official exploited having had appeal turned down (7)
I believe the answer is:
refused
'having had appeal turned down' is the definition.
'official exploited' is the wordplay.
'official' becomes 'ref' (match official in football, say).
'exploited' becomes 'used' ('used' can be a synonym of 'exploited').
'ref'+'used'='REFUSED'
(Other definitions for refused that I've seen before include "Declined, rejected" , "Not accepted" , "Was unwilling to accept" , "Said no (7)" , "turned down appeal" .)