The common link is the letters "CAR"
3.Occupation of the mouseman (4,6)
7. coo cried graham revealing heart test (14)
12. 1958 viginia mckenna film (5,3,4,4,5)
15. find a state in haircut saloon (5,8)
19. rolf harris sang about his hareem (4,10)
20. comforting greetings card character (4,4)