Steve,
It aint random, it's a perfectly fair clue, you need to split its parts up for the cryptic explanation and the definition.
CLUE: Quit publicity houses almost exhausted
Quit = The definition = Push off
Publicity / a word synonymous with publicity is PUFF (Chambers Dictionary)
houses - to house (verb) is to put in or contain or position as in (if you know mechanics) the gasket is 'housed' (positioned, placed, put or contained)in the cylinder head
exhausted = shot (if something is shot, then it has gone or has been exhausted (run out off)
almost shot is SHO (T) taken the 'T' away
Then House [as a verb](contain or put in) the SHO inside PUFF
Now you have pu (sho) ff - Pu'sh o'ff