Constable’s first to have a rotten thug arrested (6)
I believe the answer is:
caught
'arrested' is the definition.
('catch' can be a synonym of 'arrest')
'constable's first to have a rotten thug' is the wordplay.
'constable's first' becomes 'c' (1st letter of 'constable').
'to have' says to put letters next to each other.
'rotten' indicates an anagram.
'thug' is an anagram of 'ught'.
'c'+'a'+'ught'='CAUGHT'
(Other definitions for caught that I've seen before include "Nabbed" , "Overtaken - in the act?" , "Came upon" , "Got" , "Trapped or arrested" .)