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' (ad is a kind of promotion).
'among' means one lot of letters goes inside another.
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'irish' becomes 'ir' (abbreviation).
'n'+'ir'='nir'
'ad' placed within '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" .)