Guilty party, having vandalised picture gallery, leaves eagerly (7)
I believe the answer is:
culprit
'guilty party' is the definition.
(I've seen this before)
'vandalised picture gallery leaves eagerly' is the wordplay.
'vandalised' indicates anagramming the letters.
'leaves' indicates named letters should be taken away.
'picture'+'gallery'='picturegallery'
'picturegallery' with 'eagerly' taken away is 'pictulr'.
'pictulr' anagrammed gives 'CULPRIT'.
'having' is the link.
(Other definitions for culprit that I've seen before include "One perpetrating crime" , "The one to blame, guilty party" , "The one responsible for a crime" , "baddie" , "he should have conviction" .)