"exclusive affair" is a correct and usable phrase in written English.
You can use it to describe any event, gathering, or activity that has been restricted to a select group of people. For example, "The royal family will be hosting an exclusive affair to celebrate the marriage of Prince George and Princess Diana."
It was a somewhat exclusive affair.
Despite those numbers, it is a highly exclusive affair: not everyone can be part of the show.
The front row at fashion shows is a notoriously exclusive affair; only the most important fashion editors, buyers, bloggers and celebrities are awarded the coveted seats.
But the boom proved an exclusive affair: in that same period, the median income for non-elderly American households went down and the poverty rate rose.
When "The Designated Mourner" was first performed in New York 13 years ago (after being staged in London at the National Theater in 1996), it was an exclusive affair, appropriate perhaps for a chronicle of rarefied lives under siege.
The Capri festival, organized by Monda and the Naples-based documentary producer Davide Azzolini, may be an exclusive affair, but it gets lots of attention in the Italian press and is financed by the Italian government and several major corporations.
Not that these were exclusive affairs.
The literary festivals, meanwhile, were rather exclusive affairs, populated largely by highly educated English-speaking urbanites.
Like other fairs, but with signature panache, a Frieze fair also offers lectures, panels, and, of course, parties thrown by collectors and dealers, which ripple outward from exclusive affairs for high rollers to what are, essentially, free-for-alls.
As GoldDerby.com reports, an e-mail on Saturday informed voters that choosing the best documentary, best animated short and best live-action short would no longer be such exclusive affairs.
Which may be why, as New York Fashion Week kicks off today, many designers are scaling back, abandoning the extravagant productions of the past in favor of more pointedly exclusive affairs.
