Kick out and start to paddle in river and lake (5)
I believe the answer is:
expel
'kick out' is the definition.
(synonyms)
'start to paddle in river and lake' is the wordplay.
'start to' indicates taking the first letters.
'in' indicates putting letters inside.
'river' becomes 'exe' (River Exe).
'and' says to put letters next to each other.
'lake' becomes 'L' (geographical abbreviation).
The first letter of 'paddle' is 'p'.
'p' put within 'exe' is 'expe'.
'expe'+'l'='EXPEL'
'and' acts as a link.
(Other definitions for expel that I've seen before include "Discharge in disgrace" , "Force to leave" , "Throw out" , "Drive out with force" , "Possibly remove from club" .)