Lift, but not quite to Paradise! (5)
I believe the answer is:
heave
'lift' is the definition.
(I know that lift can be written as heave)
'not quite to paradise' is the wordplay.
'not quite' means to remove the last letter (most but not all of the word).
'to paradise' becomes 'heaven' (synonyms).
'heaven' with its final letter taken away is 'HEAVE'.
'but' is the link.
(Other definitions for heave that I've seen before include "Tug-of-war cry" , "Throw; haul by rope (naut.)" , "Throw with force - retch" , "Pitch" , "Be sick; rise and fall" .)