Promotion that is getting universal cheers (5)
I believe the answer is:
adieu
'cheers' is the definition.
(both can mean goodbye)
'promotion that is getting universal' is the wordplay.
'promotion' becomes 'ad' (short for advert).
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
'getting' means one lot of letters go next to another.
'universal' becomes 'u'.
'ad'+'ie'+'u'='ADIEU'
(Other definitions for adieu that I've seen before include "Ciao, in French" , "All the best" , "Fare thee well!" , "Cheerio" , "Goodbye, madame" .)