Swim across river getting wet (4)
I believe the answer is:
drip
'wet' is the definition.
(thesaurus)
'swim across river' is the wordplay.
'swim' becomes 'dip' (dip is a kind of swim).
'across' indicates putting letters inside.
'river' becomes 'r'.
'dip' placed around 'r' is 'DRIP'.
'getting' is the link.
(Other definitions for drip that I've seen before include "Fall in small droplets as from tap" , "Soppy person" , "Hospital device; weak person" , "Leak from tap" , "Fall in small drops as from wet clothes" .)