Two squares have each run up in fancy dress (8)
I believe the answer is:
froufrou
'fancy dress' is the definition.
I can't explain the remainder of the clue.
(Other definitions for froufrou that I've seen before include "(Sound made by) fancy frills on female dresses -- four/four (anag)" , "Repetitive rustling as of a silk skirt" , "Rustling or swishing as of silk skirt" , "Fussy decoration" .)