A professional person has to act with a cool head (3)
I believe the answer is:
doc
'a professional person' is the definition.
(doc is a kind of professional person)
'to act with a cool head' is the wordplay.
'to act' becomes 'do' (to do is to act or execute a task).
'with' is a charade indicator (letters next to each other).
'head' suggests taking the first letters.
The first letter of 'cool' is 'c'.
'do'+'c'='DOC'
'has' acts as a link.
(Other definitions for doc that I've seen before include "One of the seven dwarfs" , "Consultant" , "GP (colloq.)" , "Medical practitioner (abbr)" , "Disney dwarf" .)