Very wise to cover one's face (6)
I believe the answer is:
visage
'face' is the definition.
(visage is a kind of face)
'very wise to cover one's' is the wordplay.
'very' becomes 'v' (abbreviation).
'wise' becomes 'sage' ('sage' can be similar in meaning to 'wise').
'to cover' indicates putting letters inside.
'one' becomes 'i' (Roman numeral).
'v'+'sage'='vsage'
'vsage' enclosing 'i' is 'VISAGE'.
(Other definitions for visage that I've seen before include "A person's face, countenance" , "Clock" , "Mug" , "Face, aspect" .)