Worry sweet dog's been stolen (4)
I believe the answer is:
fret
'worry' is the definition.
(fretting is a kind of worrying)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for fret that I've seen before include "Anguish" , "Wear away" , "Be constantly anxious" , "Worry - pine" , "Vex oneself - part of a fingerboard" .)