Relieve the burden on the UN (6)
I believe the answer is:
unload
'relieve' is the definition.
(thesaurus)
'the burden on the un' is the wordplay.
'the burden' becomes 'load' ('load' can be a synonym of 'burden').
'on' means one lot of letters go next to another.
'load' after 'un' is 'UNLOAD'.
(Other definitions for unload that I've seen before include "Get rid" , "Take cargo off (a ship)" , "Discharge cargo" , "Remove cargo from ship or charge from gun" , "Remove goods from (a vehicle or ship)" .)