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' says the answer is hidden in the clue.
'CALM' is hidden in the letters of '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" .)