Justice of the peace that wise men disturb at rest (10)
I believe the answer is:
magistrate
'justice of the peace' is the definition.
(I've seen this in another clue)
'wise men disturb at rest' is the wordplay.
'wise men' becomes 'magi' (the three wise men from the nativity).
'disturb' indicates an anagram (I've seen 'disturbed' mean this (the order of letters is disturbed)).
'at'+'rest'='atrest'
'atrest' is an anagram of 'strate'.
'magi'+'strate'='MAGISTRATE'
'that' is the link.
(Other definitions for magistrate that I've seen before include "Person in court" , "Capital of Ethiopia" , "Law enforcer" , "your worship" , "one on the bench" .)