Stay near Sussex resort on river (5)
I believe the answer is:
hover
'stay near' is the definition.
(I've seen this before)
'sussex resort on river' is the wordplay.
'sussex resort' becomes 'hove' (I've seen this before).
'on' means one lot of letters go next to another.
'river' becomes 'r'.
'hove'+'r'='HOVER'
(Other definitions for hover that I've seen before include "Hang around (in air)" , "Remain in the air; linger" , "Wait around (like a kestrel)" , "Low flying machine (10)" , "Float hanging in the air" .)