Support goal, heading off Arab, perhaps (7)
I believe the answer is:
endorse
'support' is the definition.
(endorsing is a kind of supporting)
'goal heading off arab perhaps' is the wordplay.
'goal' becomes 'end' ('end' can be a synonym of 'goal').
'heading off' means to remove the first letter.
'arab perhaps' becomes 'horse' (arab is a kind of horse).
'horse' with its initial letter taken away is 'orse'.
'end'+'orse'='ENDORSE'
(Other definitions for endorse that I've seen before include "Put one's name to, approve" , "Countersign" , "Back, sanction" , "Give public approval of (something)" , "Say you approve" .)