Answer:
Well, first let us start off this answer with a little bit about the purpose of NATO,
NATO is an organization completely meant to protect its allies with its military and help rebuild fellow countries at a time when they're at their weakest and they do this by keeping other enemies out so now the answer.
NATO during a post-Cold War would be tasked with guarding and defending its allies while there built up their armies and securing their own grounds so they will have defense while preparing the offense.
And then when that is finished they will mainly be guarding things such as the air from enemy gun ships and stealth bombers and probably clearing out and delivering air strikes when needed on enemy fortifications and tanks.
At the same time, they will be in charge of safely relocating important people such as presidents and delivering ammo and weapons and armored vehicles to arm the soldiers that are defending their countries.