In part, Republican denies freaking out leader (9)
I believe the answer is:
president
'leader' is the definition.
(type of leader)
'in part republican denies freaking out' is the wordplay.
'in' means one lot of letters goes inside another.
'part' becomes 'pt' (abbreviation).
'republican' becomes 'R' (abbreviation in US politics).
'freaking out' indicates anagramming the letters (I've seen this in other clues).
'r'+'denies'='rdenies'
'rdenies' anagrammed gives 'residen'.
'pt' enclosing 'residen' is 'PRESIDENT'.
(Other definitions for president that I've seen before include "Head of state of a republic" , "the boss" , "club official" , "Grant perhaps" , "Leader of a republic" .)