Local man gets serene (4)
I believe the answer is:
calm
'serene' is the definition.
(synonyms)
'local man gets' is the wordplay.
'gets' indicates a hidden word.
'CALM' can be found hidden inside 'local man'.
(Other definitions for calm that I've seen before include "Serene" , "Controlled, not agitated" , "Self-possessed" , "Halcyon" , "Still or peaceful" .)