Daft tip-off given to newspaper covering earl's offence (7)
I believe the answer is:
umbrage
'offence' is the definition.
(I've seen this before)
'daft tip-off given to newspaper covering earl's' is the wordplay.
'daft' becomes 'dumb' (both can mean stupid).
'tip-off' means to remove the first letter (one tip of the word is removed).
'given to' says to put letters next to each other.
'newspaper covering' becomes 'rag' (I can't explain this - if you can you should give a lot more credence to this answer).
'earl' becomes 'e'.
'dumb' with its initial letter removed is 'umb'.
'umb'+'rag'+'e'='UMBRAGE'
(Other definitions for umbrage that I've seen before include "Take this to feel offence" , "Indignation" , "Suspicion of injury" , "Offence, annoyance" , "Take this to be offended" .)