Arab territory that makes me turn cross (7)
I believe the answer is:
emirate
'arab territory' is the definition.
(I've seen this before)
'me turn cross' is the wordplay.
'turn' says the letters should be written in reverse.
'cross' becomes 'irate' (I've seen this before).
'me' written backwards gives 'em'.
'em'+'irate'='EMIRATE'
'that makes' acts as a link.
(Other definitions for emirate that I've seen before include "One of the Gulf states" , "state of Middle East?" , "Independent Islamic state" , "Gulf state, perhaps" , "Foreign office" .)