Farewell promotion Independent editor initially refused essentially (5)
I believe the answer is:
adieu
'farewell' is the definition.
(adieu is a kind of farewell)
'promotion independent editor initially refused essentially' is the wordplay.
'promotion' becomes 'ad' (short for advert).
'initially' says to take the initial letters.
'essentially' means to look at the middle letters.
The central letter of 'refused' is 'u'.
The initial letters of 'independent editor' is 'ie'.
'ad'+'ie'+'u'='ADIEU'
(Other definitions for adieu that I've seen before include "Gallic goodbye" , "Goodbye to the French" , "cheers" , "Vale" , "Ciao, in French" .)