Difficult conflict finally resolved after a week (7)
I believe the answer is:
awkward
'difficult' is the definition.
(I've seen this before)
'conflict finally resolved after a week' is the wordplay.
'conflict' becomes 'war' (war is a kind of conflict).
'finally resolved' becomes 'd' (I can't explain this - if you can you should believe this answer much more).
'after' says to put letters next to each other.
'week' becomes 'wk' (common abbreviation).
'war'+'d'='ward'
'a'+'wk'='awk'
'ward' put after 'awk' is 'AWKWARD'.
(Other definitions for awkward that I've seen before include "Inelegant; tricky" , "inconvenient" , "Embarrassed" , "Difficult to handle" , "Gauche or uncoordinated" .)