Tim goes out showing vanity (7)
I believe the answer is:
egotism
'vanity' is the definition.
(I know that egotism is a type of vanity)
'tim goes out' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'tim'+'goes'='timgoes'
'timgoes' anagrammed gives 'EGOTISM'.
'showing' acts as a link.
(Other definitions for egotism that I've seen before include "Items go (anag.)" , "Obsession with oneself" , "Self-obsession" , "Self-importance" , "Selfishness" .)