Vie with Arabs in a way that is irritating (8)
I believe the answer is:
abrasive
'is irritating' is the definition.
(I've seen this before)
'vie with arabs in a way' is the wordplay.
'with' says to put letters next to each other.
'in a way' indicates an anagram.
'vie'+'arabs'='viearabs'
'viearabs' anagrammed gives 'ABRASIVE'.
'that' acts as a link.
(Other definitions for abrasive that I've seen before include "Harsh - chafing" , "Emery paper or steel wool, say" , "Causing irritation" , "Like pumice - rough in manner" , "Harsh - scratchy" .)