Good man's come down with overwork (6)
I believe the answer is:
strain
'overwork' is the definition.
(thesaurus)
'good man's come down' is the wordplay.
'good man' becomes 'st'.
'come down' becomes 'rain' (raining is a kind of coming down).
'st'+'rain'='STRAIN'
'with' is the link.
(Other definitions for strain that I've seen before include "'Stress, tension (6)'" , "Put through a perforated device to separate" , "Screen" , "Family - stress - air - force" , "Pass through a filter" .)