Party fringes in torment, ailing badly (8)
I believe the answer is:
litigant
'party' is the definition.
(litigant is a kind of party)
'fringes in torment ailing badly' is the wordplay.
'fringes in' says to hollow out the word (remove centre letters) (fringe can mean the edge of something).
'badly' is an anagram indicator.
'torment' with its centre taken out is 'tt'.
'tt'+'ailing'='ttailing'
'ttailing' with letters rearranged gives 'LITIGANT'.
(Other definitions for litigant that I've seen before include "One going to law" , "Person engaged in lawsuit" , "One who goes to law" , "One who takes a lawsuit" , "Plaintiff" .)