Laugh about publicity account problem (8)
I believe the answer is:
headache
'problem' is the definition.
(I've seen this before)
'laugh about publicity account' is the wordplay.
'laugh' becomes 'he-he' (sound of a laugh).
'about' means one lot of letters goes inside another.
'publicity' becomes 'ad' (advert).
'account' becomes 'ac' (abbreviation for account).
'ad'+'ac'='adac'
'hehe' enclosing 'adac' is 'HEADACHE'.
(Other definitions for headache that I've seen before include "Informally a worrying problem - take an asprin" , "Major problem" , "Serious problem?" , "nasty problem" , "Severe problem" .)