Implement argument over university city (7)
I believe the answer is:
spatula
'implement' is the definition.
(I know that spatula is a type of hand tool)
'argument over university city' is the wordplay.
'argument' becomes 'spat' (a spat is a disagreement or argument).
'over' means one lot of letters go next to another (in a down clue, some letters go over others).
'university' becomes 'U' (abbreviation as in UMass).
'city' becomes 'LA' (Los Angeles).
'spat'+'u'+'la'='SPATULA'
(Other definitions for spatula that I've seen before include "Broad spoon" , "Thin tool for mixing or spreading soft substances" , "flat mixer" , "Lab mixing implement" , "Food turner with flexible blade" .)