A Sligo jig
Original recording here: http://www.archive.org/details/PaddySweenyRogersJigVillageJig Recorded by Paddy Sweeney, November 26, 1937. I’ll transcribe the other tune in his medley, the Village Jig, as well. Both are lovely tunes which don’t seem to be in any collection, online or otherwise.
Now I remember that the 1st part here is also that of the Bridal Jig: https://thesession.org/tunes/1000 As noted in the comments that tune was also recorded by Paddy Killoran and his Pride of Erin Orchestra - where Sweeney played 2nd fiddle. Must have been confusing to keep all these tunes straight!