Rein in dog on dog (7)
I believe the answer is:
curtail
'rein in' is the definition.
(thesaurus)
'dog on dog' is the wordplay.
'dog' becomes 'cur' (both can mean a despicable person).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'dog' becomes 'tail' (synonyms).
'cur'+'tail'='CURTAIL'
(Other definitions for curtail that I've seen before include "Cut short like canine appendage" , "Abbreviate" , "Shorten, abridge" , "make shorter" , "Cut short (an activity)" .)