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 wordplay.
'fellows' becomes 'ff'.
'turned' says the letters should be written in reverse.
'first' says to put letters next to each other.
'up' back-to-front is 'pu'.
'ff' after 'pu' is 'PUFF'.
(Other definitions for puff that I've seen before include "out of which pants come?", "Light cake; type of sleeve", "Gust", "Quick emission of smoke etc", "plug", "pastry dessert", "Pull", "Light pastry; some wind", "Breathe in short gasps" and "Gasp".)