Rise as Justice of the Peace stifles sign of hesitation (4)
I believe the answer is:
jump
'rise' is the definition.
(jumping is a kind of rising)
'justice of the peace stifles sign of hesitation' is the wordplay.
'justice of the peace' becomes 'jp'.
'stifles' indicates putting letters inside.
'sign of hesitation' becomes 'um'.
'jp' placed around 'um' is 'JUMP'.
'as' acts as a link.
(Other definitions for jump that I've seen before include "Suddenly rise" , "Spring" , "Sudden large increase" , "Vault, bound" , "Suddenly increase" .)