Drive to clean out, with no pressure (4)
I believe the answer is:
urge
'drive' is the definition.
(I've seen this in another clue)
'clean out with no pressure' is the wordplay.
'clean out' becomes 'purge' (I've seen this in another clue).
'with no' indicates named letters should be taken away.
'pressure' becomes 'p' (abbreviation).
'purge' with 'p' taken out is 'URGE'.
'to' is the link.
(Other definitions for urge that I've seen before include "Advocate" , "Impel, egg on" , "Compulsion; egg on" , "Egg on, encourage to proceed" , "Yen" .)