Longing to remove initiator of political clean-up (4)
I believe the answer is:
urge
'longing' is the definition.
(I've seen this before)
'to remove initiator of political clean-up' is the wordplay.
'to remove initiator of' means to remove the first letter (the letter which begins or initiates the word).
'political clean-up' becomes 'purge' (as in a purge of political rivals).
'purge' with its first letter taken away is 'URGE'.
(Other definitions for urge that I've seen before include "Yen" , "Plead" , "'Spur on, encourage (4)'" , "Try hard to persuade, advise earnestly" , "Strongly encourage" .)