This is a Scottish reel I heard played by piano-accordionist Phil Cunningham on the album he made with his brother John, "Against The Storm". It has a known composer, but a cursory look at likely websites has not turned him up.
The second part is very much like that of Julia Delaney’s: https://thesession.org/tunes/589
Composed by James Macintosh of Dunkeld, Perthshire. I don’t know a lot about him, but I have a copy of a small collection of tunes he published in 1930, which includes "Birkenburn". It’s not too far away from the Cunninghams’ version.
The second reel in the set from ‘Against the Storm’ is "Loch Ordie":