The vaccine does not prevent people catching the virus - it simply reduces the chances of them becoming seriously unwell. Furthermore it only reduces (and does not prevent) them from spreading the disease to others.
Mass international air travel will not resume until the vaccine has been rolled out worldwide and the requirement for testing and quarantine on arrival have been removed. The latter part of this is going to be extremely difficult, since many countries seem to have adopted a 'Covid-Zero' strategy, which is just not compatible with open borders.
The whole thing will take years, as opposed to months to resolve.
I see the short-medium term future as being regional travel areas or travel corridors between countries with agreed Covid protocols. And I think the long-haul business market will probably never fully return since everyone has realised pretty much the same effect can be achieved through MS Teams