Attempt to cover new dilemma (4)
I believe the answer is:
bind
'dilemma' is the definition.
(thesaurus)
'attempt to cover new' is the wordplay.
'attempt to' becomes 'bid'.
'cover' is an insertion indicator.
'new' becomes 'n'.
'bid' enclosing 'n' is 'BIND'.
(Other definitions for bind that I've seen before include "Impose a contractual obligation on (someone)" , "Tie up; annoyance" , "Join or fasten together" , "Restrict" , "difficulty" .)