Publicity fellows turned up first (4)
I believe the answer is:
Here is my best explanation:
'publicity' is the definition.
'fellows turned up first' is the subsidiary indication.
'fellows' becomes 'ff'.
'turned' shows that the letters should be reversed in order.
'first' says to put letters next to each other.
'up' reversed gives 'pu'.
'ff' put after 'pu' is 'puff'.
(Other definitions for puff that I've seen before include "Gust", "Advertisement; smoke a cigarette", "Blow", "Breath", "Short gust of wind", "Exaggerated praise (for promotional purposes?)", "Short blow (of smoke)", "Sudden breath; advert", "Gasp" and "Swell".)