Ineffectual person has gone mad, showing deep resentment (7)
I believe the answer is:
dudgeon
'deep resentment' is the definition.
(I've seen this before)
'ineffectual person has gone mad' is the wordplay.
'ineffectual person' becomes 'dud' (I've seen this before).
'has' says to put letters next to each other.
'mad' indicates anagramming the letters.
'gone' with letters rearranged gives 'geon'.
'dud'+'geon'='DUDGEON'
'showing' is the link.
(Other definitions for dudgeon that I've seen before include "State of being (highly) aggrieved" , "Umbrage" , "huff" , "indignant state" , "Feeling of intense indignation" .)