Here is a forum discussion of the tune:

harpcolumn forum topic - Origin of "O'Carolan's Air"

The post by Biagio on March 11, 2019 at 1:07 pm says he/she? "asked a few Irish music scholars. Here’s the consensus:

“We don’t know, but it is not consistent in style with his other compositions, nor is it any known tune by him. It could be a later ‘imitation’ for copyright or similar reasons, written as a tribute, or a modern composition intended to suggest his style. If Betty Paret cannot be reached it may be the latter (by her).”

It's funny, well it is to me anyway, that near the beginning of the thread someone states that it is Carolan's Welcome, even though it sounds nothing like that lovely, distinctive tune.

Curiouser and curiouser, but I'm tending towards the idea that it was written as a tribute to Turlough O'Carolan.