Palm-greasing bachelor tucking into cheese by railway (7)
I believe the answer is:
bribery
'palm-greasing' is the definition.
(I've seen this before)
'bachelor tucking into cheese by railway' is the wordplay.
'bachelor' becomes 'b' (abbreviation e.g. BA=Bachelor of Arts).
'tucking into' indicates putting letters inside.
'cheese' becomes 'brie' (Brie is an example).
'by' is a charade indicator (letters next to each other).
'railway' becomes 'ry' (abbreviation for railway).
'b' inserted inside 'brie' is 'bribe'.
'bribe'+'ry'='BRIBERY'
(Other definitions for bribery that I've seen before include "criminal offence" , "Illegal offering of inducements" , "Giving of a back-hander" , "The use of money to persuade" , "Graft" .)