Flat by centre of quad in Italian city (5)
I believe the answer is:
padua
'italian city' is the definition.
(I've seen this before)
'flat by centre of quad' is the wordplay.
'flat' becomes 'pad' (a person's home).
'by' is a charade indicator (letters next to each other).
'centre of' says to take the centre.
The middle letters of 'quad' are 'ua'.
'pad'+'ua'='PADUA'
'in' acts as a link.
(Other definitions for padua that I've seen before include "City of N. Italy" , "Italian city near Venice" , "Italian city of St Anthony" , "North-eastern Italian city" , "City in northeast Italy" .)