Offence of rum-running securing bishop a number of years (7)
I believe the answer is:
umbrage
'offence' is the definition.
(I know that offence can be written as umbrage)
'rum-running securing bishop a number of years' is the wordplay.
'running' is an anagram indicator.
'securing' means one lot of letters goes inside another.
'bishop' becomes 'B' (chess abbreviation).
'a number of years' becomes 'age' (I've seen this in another clue).
'rum' is an anagram of 'umr'.
'umr' placed around 'b' is 'umbr'.
'umbr'+'age'='UMBRAGE'
'of' acts as a link.
(Other definitions for umbrage that I've seen before include "Offence, annoyance" , "Offence that's usually taken" , "The sulks" , "Feeling of offence" , "Suspicion of injury" .)