Italian food around a public square (6)
I believe the answer is:
piazza
'public square' is the definition.
(piazza is a kind of public square)
'italian food around a' is the wordplay.
'italian food' becomes 'pizza' (I've seen this before).
'around' means one lot of letters goes inside another.
'pizza' enclosing 'a' is 'PIAZZA'.
(Other definitions for piazza that I've seen before include "Where Italians may gather" , "3 down" , "Public square in Italian town" .)