Walker’s extremely smart luxury car (8)
I believe the answer is:
stroller
'walker's' is the definition.
(stroller is a kind of walker)
'extremely smart luxury car' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'luxury car' becomes 'roller' (short for Rolls Royce).
'smart' with its middle taken out is 'st'.
'st'+'roller'='STROLLER'
(Other definitions for stroller that I've seen before include "baby carriage" , "One wandering about" , "Walker" , "Child's vehicle" , "He walks" .)