Fuel price beginning to drop (4)
I believe the answer is:
feed
'fuel' is the definition.
(thesaurus)
'price beginning to drop' is the wordplay.
'price' becomes 'fee' (I've seen this in other clues).
'beginning to' suggests taking the first letters.
The initial letter of 'drop' is 'd'.
'fee'+'d'='FEED'
(Other definitions for feed that I've seen before include "Provide food" , "take courses" , "Take food" , "Provide something to eat" , "Eat; pass (a ball) to another player" .)