Remove permit in river (6)
I believe the answer is:
delete
'remove' is the definition.
(deleting is a kind of removing)
'permit in river' is the wordplay.
'permit' becomes 'let' (synonyms).
'in' means one lot of letters goes inside another.
'river' becomes 'dee' (River Dee).
'let' inserted inside 'dee' is 'DELETE'.
(Other definitions for delete that I've seen before include "Key" , "Expunge, erase" , "Blot out or erase" , "Strike out (text)" , "Obliterate" .)