Sport to reach out to railway (7)
I believe the answer is:
archery
'sport' is the definition.
(archery is a kind of sport)
'reach out to railway' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'to railway' becomes 'ry' (abbreviation for railway).
'reach' is an anagram of 'arche'.
'arche'+'ry'='ARCHERY'
'to' acts as a link.
(Other definitions for archery that I've seen before include "Target sport - Olympic event in from 1900-08, in 1920 and since 1972" , "Arrow-shooting" , "Bow and arrow sport" , "The sport of bowmen" , "Bowman's sport" .)