Steal from egghead to get gown (4)
I believe the answer is:
robe
'gown' is the definition.
(I know that gown can be written as robe)
'steal from egghead' is the wordplay.
'steal from' becomes 'rob' (I've seen this in another clue).
'egghead' becomes 'e' (head letter of 'egg').
'rob'+'e'='ROBE'
'to get' acts as a link.
(Other definitions for robe that I've seen before include "Any loose flowing garment" , "judge's garment" , "Loose outer garment" , "Old cloak for Boer" , "Ceremonial garment, clothe" .)