Local man keeps cool (4)
I believe the answer is:
calm
'cool' is the definition.
(I've seen this before)
'local man keeps' is the wordplay.
'keeps' indicates a hidden word.
'CALM' is hidden within 'local man'.
(Other definitions for calm that I've seen before include "'Tranquil, placid (4)'" , "Composed or free from storms" , "Composure or serenity" , "Placid and unruffled" , "Peaceful, not excited" .)