Courtesy shown by Greek character to lady by railway (8)
I believe the answer is:
chivalry
'courtesy' is the definition.
(chivalry is a kind of courtesy)
'greek character to lady by railway' is the wordplay.
'greek character' becomes 'chi' (letter from the Greek alphabet).
'to lady' becomes 'val' (**).
'by' means one lot of letters go next to another.
'railway' becomes 'ry' (abbreviation for railway).
'chi'+'val'+'ry'='CHIVALRY'
'shown by' acts as a link.
(Other definitions for chivalry that I've seen before include "Medieval knightly system of honour" , "Almost defunct code of courtesy towards women" , "Gentlemanliness" , "Knightly principles" , "Knightliness" .)