Notwithstanding, it's a vestment to fasten up (6)
I believe the answer is:
albeit
'notwithstanding' is the definition.
(I've seen this in another clue)
'a vestment to fasten up' is the wordplay.
'a vestment' becomes 'alb' (alb is a kind of vestment).
'to' is a charade indicator (letters next to each other).
'fasten' becomes 'tie' (tying is a kind of fastening).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'tie' reversed gives 'eit'.
'alb'+'eit'='ALBEIT'
'it's' acts as a link.
(Other definitions for albeit that I've seen before include "Although, despite" , "'Even if, although (6)'" , "Conjunction meaning although" , "In spite of the fact that" , "Although, nevertheless" .)