Rigidly old-fashioned (5)
(Other definitions for square that I've seen before include "Level - shape - piazza - stuffy" , "Centre of cricket ground" , "uncool" , "Type of rectangle" , "New York Times, for example" .)
'rigidly old-fashioned' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for fusty that I've seen before include "Smelling stale or damp" , "Stale-smelling" .)