Driver to get damp going round hill (8)
I believe the answer is:
motorist
'driver' is the definition.
(motorist is a kind of driver)
'damp going round hill' is the wordplay.
'damp' becomes 'moist' ('moist' can be a synonym of 'damp').
'going round' indicates putting letters inside.
'hill' becomes 'tor' (tor is a kind of hill).
'moist' enclosing 'tor' is 'MOTORIST'.
'to get' acts as a link.
(Other definitions for motorist that I've seen before include "One relying on car" , "Car-driver" , "One driving" , "Woman taking mini" , "Car driver" .)