Quickly paid running into railway (7)
I believe the answer is:
rapidly
'quickly' is the definition.
(I know that quickly can be written as rapidly)
'paid running into railway' is the wordplay.
'running' indicates an anagram (the letters run around to different places).
'into' indicates putting letters inside.
'railway' becomes 'rly'.
'paid' is an anagram of 'apid'.
'apid' put inside 'rly' is 'RAPIDLY'.
(Other definitions for rapidly that I've seen before include "right off the bat" , "Speedily" , "With great speed" , "Fast" , "At a great rate" .)