Have argument about rook with an ascetic? (7)
I believe the answer is:
spartan
'ascetic?' is the definition.
(I know that ascetic can be written as spartan)
'have argument about rook with an' is the wordplay.
'have argument' becomes 'spat' (I can't justify this - if you can you should give a lot more credence to this answer).
'about' is an insertion indicator.
'rook' becomes 'R' (chess abbreviation).
'with' says to put letters next to each other.
'spat' going around 'r' is 'spart'.
'spart'+'an'='SPARTAN'
(Other definitions for spartan that I've seen before include "Not comfortable" , "Austere - like Lysander?" , "Bleak - rigorous - austere" , "Frugal" , "Old citizen" .)