Refuse to acknowledge one's outwardly depressed (6)
I believe the answer is:
disown
'refuse to acknowledge' is the definition.
(I've seen this before)
'one's outwardly depressed' is the wordplay.
'one's' becomes 'I's' (Roman numeral).
'outwardly' indicates putting letters inside (some letters go outside others).
'depressed' becomes 'down' (synonyms).
'is' put within 'down' is 'DISOWN'.
(Other definitions for disown that I've seen before include "Disclaim or deny" , "Repudiate, cast off" , "Refuse to be associated with (something/someone)" , "Refuse to be associated with (a person)" , "Refuse to be connected with" .)