Hovering, having finished (4)
I believe the answer is:
over
This clue is a double definition.
'hovering' is the first definition.
(I've seen this in another clue)
'finished' is the second definition.
(over can mean finished or ended)
'having' acts as a link.
(Other definitions for over that I've seen before include "Unit of test" , "Six consecutive bowls in cricket" , "Finished like cricket period" , "Finished like round of bowling in cricket" , "See 18" .)