Greek character, railman, regularly skirts public house (5)
I believe the answer is:
alpha
'greek character' is the definition.
(letter from the Greek alphabet)
'railman regularly skirts public house' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'skirts' means one lot of letters goes inside another (skirt can mean to go around).
'public house' becomes 'ph' (abbreviation).
The alternating letters of 'railman' are 'ala'.
'ala' enclosing 'ph' is 'ALPHA'.
(Other definitions for alpha that I've seen before include "Top star" , "Early testing stage for new software or hardware" , "star outshining the others" , "Brilliant star" , "Beginning" .)