Desire purification - but not at first (4)
I believe the answer is:
urge
'desire' is the definition.
(thesaurus)
'purification but not at first' is the wordplay.
'purification' becomes 'purge'.
'but not at first' means to remove the first letter.
'purge' with its first letter taken away is 'URGE'.
(Other definitions for urge that I've seen before include "Advise strongly or prod" , "Advise earnestly, prod" , "Strongly recommend; impulse" , "Encourage or entreat earnestly" , "Strong impulse, desire" .)