Extra cost keeping car in drive outside entrance to home (9)
I believe the answer is:
surcharge
'extra cost' is the definition.
(a surcharge is an additional cost)
'car in drive outside entrance to home' is the wordplay.
'in' is an insertion indicator.
'drive' becomes 'surge' ().
'outside' means one lot of letters goes inside another.
'entrance to' says to take the initial letters.
The first letter of 'home' is 'h'.
'car' going within 'surge' is 'surcarge'.
'surcarge' placed around 'h' is 'SURCHARGE'.
'keeping' is the link.
(Other definitions for surcharge that I've seen before include "Additional sum demanded" , "additional amount" , "Excess fee" , "More to pay" , "supplement" .)