Reprobate Dolly pursues Sooty (5,5)
I believe the answer is:
black sheep
'reprobate' is the definition.
(black sheep is a kind of reprobate)
'dolly pursues sooty' is the wordplay.
'dolly' becomes 'sheep' (Dolly the Sheep is an example).
'pursues' says to put letters next to each other.
'sooty' becomes 'black' ('black' can be similar in meaning to 'sooty').
'sheep' after 'black' is 'BLACK SHEEP'.
(Other definitions for black sheep that I've seen before include "Unprincipled reprobate - nursery rhyme animal" , "Dodgy character" , "Disreputable relative" , "Disgraced family member" , "Source of family shame" .)