Undergarment almost completely chaste (6)
I believe the answer is:
vestal
'chaste' is the definition.
('vestal' can be similar in meaning to 'chaste')
'undergarment almost completely' is the wordplay.
'undergarment' becomes 'vest' (vest is a kind of undergarment).
'almost' means to remove the last letter (most of the word but not all of it).
'completely' becomes 'all' ('all' can be a synonym of 'completely').
'all' with its last letter taken off is 'al'.
'vest'+'al'='VESTAL'
(Other definitions for vestal that I've seen before include "Fat for candles/soap" , "Modest female" , "Woman dedicated to celibacy" , "Consecrated Roman virgin" , "Chaste (Roman priestess)" .)