Most rotten, having to jog (4)
I believe the answer is:
trot
'to jog' is the definition.
('trot' can be a synonym of 'jog')
'most rotten having' is the wordplay.
'having' indicates a hidden word.
'TROT' is hidden within 'most rotten'.
(Other definitions for trot that I've seen before include "Jog along" , "Steady gentle run" , "Horse's pace - Communist" , "Slowish run, of horse or person" , "Horse's steady pace" .)