Swag closer relative pinched (5)
I believe the answer is:
gaunt
'pinched' is the definition.
(I know that pinched can be written as gaunt)
'swag closer relative' is the wordplay.
'closer' indicates one should take the final letters (the letter which 'closes' the word).
'relative' becomes 'aunt' (aunt is a type of relative).
The final letter of 'swag' is 'g'.
'g'+'aunt'='GAUNT'
(Other definitions for gaunt that I've seen before include "Hollow-eyed, skinny" , "Drawn" , "Grim" , "Bleak" , "birthplace of Edward's son" .)