A quip oddly used by Irish national (5)
I believe the answer is:
iraqi
'national' is the definition.
(I've seen this before)
'a quip oddly used by irish' is the wordplay.
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
'used by' says to put letters next to each other.
'irish' becomes 'IR' (abbreviation).
The alternating letters of 'quip' are 'qi'.
'a'+'qi'='aqi'
'aqi' after 'ir' is 'IRAQI'.
(Other definitions for iraqi that I've seen before include "Probably a Muslim" , "Baghdadi, perhaps" , "native of troubled land" , "Middle Easterner" , "Nationality of citizen of Baghdad" .)