Dog that's well trained asleep in back of car (8,7)
I believe the answer is:
springer spaniel
'dog' is the definition.
(springer spaniel is a kind of dog)
'well trained asleep in back of car' is the wordplay.
'well' becomes 'spring' (a well is a spring of water).
'trained' indicates anagramming the letters (train can mean to shape or manipulate).
'back of' suggests the final letters.
The final letter of 'car' is 'r'.
'asleep'+'in'+'r'='asleepinr'
'asleepinr' is an anagram of 'erspaniel'.
'spring'+'erspaniel'='SPRINGER SPANIEL'
'that's' is the link.
(Other definitions for springer spaniel that I've seen before include "breed of dog" , "one used to raise game" , "might this be barking?" .)