Cover payment of leader with a different kind of hesitation (7)
I believe the answer is:
premium
'cover' is the definition.
(insurance)
'payment of leader with a different kind of hesitation' is the wordplay.
'of leader' says to take the initial letters (I've seen 'leaders' mean this).
'with' means one lot of letters go next to another.
'a different kind of' becomes 'remi' (I can't justify this - if you can you should give a lot more credence to this answer).
'hesitation' becomes 'um' (sound made when hesitating).
The initial letter of 'payment' is 'p'.
'p'+'remi'+'um'='PREMIUM'
(Other definitions for premium that I've seen before include "Extra cost of something in short supply" , "Award" , "highest quality" , "best quality" , "Insurance charge" .)