Air_pig,
No, it is already a member of the NATO Partnership for Peace programme.
And of course, already has the above mentioned agreement with the UK about penetrating Irish airspace, which, by its very nature, implies that Ireland would have to be provided with early warning of any threat.
https://en.wikipedia.org/wiki/Ireland–NATO_relations
https://www.irishtimes.com/news/irel...told-1.4580389
Cooperation and coordination with neighbouring countries does not require joining the military alliance.
https://www.oireachtas.ie/en/debates.../2020-10-08/1/