Broken-down gents is man's task (10)
I believe the answer is:
assignment
'task' is the definition.
(thesaurus)
'broken-down gents is man's' is the wordplay.
'broken down' indicates anagramming the letters.
'gents'+'is'+'man'='gentsisman'
'gentsisman' is an anagram of 'ASSIGNMENT'.
(Other definitions for assignment that I've seen before include "job" , "Duty to be done" , "Task or duty" , "Task, piece of work" .)