Some press campaign fraud (4)
I believe the answer is:
scam
'fraud' is the definition.
(I know that scam is a type of cheat)
'some press campaign' is the wordplay.
'some' indicates a hidden word (some of the parts of the word are used).
'SCAM' is hidden within 'press campaign'.
(Other definitions for scam that I've seen before include "'A con, deception (4)'" , "rook" , "Screw" , "Fraud, dishonest scheme" , "Swindle (sl.)" .)