Partially divide ten territories, lessening hostility (7)
I believe the answer is:
detente
'lessening hostility' is the definition.
(period of improved relations)
'partially divide ten territories' is the wordplay.
'partially' says the answer is hidden in the clue.
'DETENTE' can be found hidden inside 'divide ten territories'.
(Other definitions for detente that I've seen before include "relaxation" , "Relaxed relations" , "Easing of strained relations" , "Easing of hostility between countries" , "Easing of international hostility" .)