Dress up to show off (4)
I believe the answer is:
brag
'show off' is the definition.
'dress up' is the wordplay.
'dress' becomes 'garb' ('garb' can be a synonym of 'dress').
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'garb' back-to-front is 'BRAG'.
'to' is the link.
(Other definitions for brag that I've seen before include "game of bluff" , "Card game - boast" , "Boast, exaggerate" , "game, making > boast" , "Idle talk" .)