Minimum promotion among Northern Irish (5)
I believe the answer is:
nadir
'minimum' is the definition.
(thesaurus)
'promotion among northern irish' is the wordplay.
'promotion' becomes 'ad' (short for advert).
'among' is an insertion indicator (inserted letters are placed among others).
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'irish' becomes 'IR' (abbreviation for Irish).
'n'+'ir'='nir'
'ad' put into 'nir' is 'NADIR'.
(Other definitions for nadir that I've seen before include "Rock bottom" , "Lowest point, or time of deepest depression." , "Very bottom, farthest from zenith" , "Point opposite the zenith" , "lowest of the low" .)