One appealing charge in Little River (10)
I believe the answer is:
petitioner
'one appealing' is the definition.
'charge in little river' is the wordplay.
'charge' becomes 'ion' (an ion is a charged particle).
'in' means one lot of letters goes inside another.
'little' becomes 'petite' (similar in meaning).
'river' becomes 'r'.
'ion' placed inside 'petite' is 'petitione'.
'petitione'+'r'='PETITIONER'
(Other definitions for petitioner that I've seen before include "One making appeal to authority" , "One with a suit" .)