Dog turned up in the car, thankfully (5)
I believe the answer is:
trace
'dog' is the definition.
(I know that trace is a kind of dog)
'turned up in the car thankfully' is the wordplay.
'turned up' shows that the letters should be reversed in order.
'in' says the answer is hidden in the clue.
'ecart' can be found hidden inside 'the car thankfully'.
'ecart' reversed gives 'TRACE'.
(Other definitions for trace that I've seen before include "Cater (anag.)" , "Find by investigation" , "Very small amount that can only just be detected" , "indicator" , "Vestige, hint" .)