Peacekeepers having time and particular approach to sort things out (8)
I believe the answer is:
untangle
'sort things out' is the definition.
(to untangle is to resolve or sort out)
'peacekeepers having time and particular approach' is the wordplay.
'peacekeepers' becomes 'UN' (United Nations, peacekeeping organisation).
'having' means one lot of letters go next to another.
'time' becomes 't' (abbreviation).
'and' means one lot of letters go next to another.
'particular approach' becomes 'angle' (as in a journalist's angle on a story).
'un'+'t'+'angle'='UNTANGLE'
'to' acts as a link.
(Other definitions for untangle that I've seen before include "Make free from disorder" , "Straighten out, free from mesh" , "Make free from confusion" , "Extricate" , "'Unpick, unravel (8)'" .)