Resentment once of failure, gone bad (7)
I believe the answer is:
Here is my best explanation:
'resentment once' is the definition.
(archaic term for a resentment)
'failure gone bad' is the subsidiary indication.
'failure' becomes 'dud' (dud is a kind of failure).
'bad' indicates an anagram.
'gone' with letters rearranged gives 'geon'.
'of' is the link.
(Other definitions for dudgeon that I've seen before include "Umbrage", "Angry feeling", "Indignation", "Offended indignation", "Resentment", "Sullenness", "feeling of resentment", "Deep resentment", "deep resentment" and "State of being (highly) aggrieved".)