Old car loses its initial value (4)
I believe the answer is:
rate
'value' is the definition.
(both can mean to esteem)
'old car loses its initial' is the wordplay.
'old car' becomes 'crate' (informal term for an old car).
'loses its initial' means to remove the first letter.
'crate' with its first letter removed is 'RATE'.
(Other definitions for rate that I've seen before include "See 11" , "Tear (anag.)" , "Charge per unit" , "The speed of movement" , "Admire" .)