Grows swans by river (7)
I believe the answer is:
deepens
'grows' is the definition.
(deepen can mean to grow or become more significant)
'swans by river' is the wordplay.
'swans' becomes 'pens' (pen can mean a female swan).
'by' is a charade indicator (letters next to each other).
'river' becomes 'dee' (River Dee).
'pens' put after 'dee' is 'DEEPENS'.
(Other definitions for deepens that I've seen before include "Intensifies" , "Dredges" , "gets stronger" , "increases" , "Make further down, say ditch" .)