In favour of poet's publicity campaign (9)
I believe the answer is:
promotion
'publicity campaign' is the definition.
(I've seen this before)
'in favour of poet's' is the wordplay.
'in favour of' becomes 'pro' (I've seen this before).
'poet' becomes 'motion' (I've seen this in other clues).
'pro'+'motion'='PROMOTION'
(Other definitions for promotion that I've seen before include "Step up" , "upgrading" , "movement?" , "sales campaign" , "Publicity campaign" .)