Vestment about to be given extravagant lining (5)
I believe the answer is:
cotta
'vestment' is the definition.
(type of garment worn by priests)
'to be given extravagant lining' is the wordplay.
'to be given' becomes 'ca' (I can't justify this - if you can you should believe this answer much more).
'extravagant' becomes 'ott' (I've seen this in other clues).
'lining' indicates putting letters inside.
'ca' enclosing 'ott' is 'COTTA'.
'about' is the link.
(Other definitions for cotta that I've seen before include "Short church garment" , "Vestment" , "Catholic church garment" , "tunic for the priest" , "Short surplice worn by Catholic priests -- to act (anag)" .)