Gad about, dashing across Roman square (9)
I believe the answer is:
gallivant
'gad about' is the definition.
(I've seen this before)
'dashing across roman square' is the wordplay.
'dashing' becomes 'gallant' (synonyms).
'across' means one lot of letters goes inside another.
'roman square' becomes 'IV' (Roman numerals for four, a square number).
'gallant' enclosing 'iv' is 'GALLIVANT'.
(Other definitions for gallivant that I've seen before include "Gad about, seeking pleasure" , "Go in search of fun" , "Pleasure-seek" , "jaunt" , "Flit about" .)