Undergarment nearly completely chaste (6)
I believe the answer is:
vestal
'chaste' is the definition.
(similar in meaning)
'undergarment nearly completely' is the wordplay.
'undergarment' becomes 'vest' (vest is a kind of undergarment).
'nearly' means to remove the last letter.
'completely' becomes 'all' (synonyms).
'all' with its last letter taken away is 'al'.
'vest'+'al'='VESTAL'
(Other definitions for vestal that I've seen before include "Virgin charged with keeping alight the fire on the altar to a Roman goddess" , "Chaste (Roman priestess)" , "Woman dedicated to celibacy" , "Fat for candles/soap" , "Modest female" .)