Eat out on badly run vessel (3,3)
I believe the answer is:
tea urn
'vessel' is the definition.
(tea urn is a kind of vessel)
'eat out on badly run' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'on' says to put letters next to each other.
'badly' is an anagram indicator.
'eat' is an anagram of 'tea'.
'run' with letters rearranged gives 'urn'.
'tea'+'urn'='TEA-URN'
(Other definitions for tea urn that I've seen before include "samovar" , "vessel in mess?" , "large vessel for drink" , "Nature (anag)" , "Container for brewing up in quantity" .)