In the direction of Georgia's garment (4)
I believe the answer is:
toga
'garment' is the definition.
(toga is a kind of garment)
'in the direction of georgia's' is the wordplay.
'in the direction of' becomes 'to'.
'georgia' becomes 'GA' (abbreviation).
'to'+'ga'='TOGA'
(Other definitions for toga that I've seen before include "Roman male garb" , "Outer garment" , "Roman citizen's robe" , "Old-style dress" , "Got a robe for an old Roman" .)