Technically you substantially reproduce both the O'Carolan and the prior arrangement.

O'Carolan's copyright has expired.

Has that of the previous arrangement?

Since you are adapting the previous arangement, if it is in copyright you will need express permission - MCPS rights do not normally extend to changing a work. THe split will be part of the deal.

Then you register it with MCPS as "Trad, arr [previous arranger],[your name] and notify them of the split.

If you and the previous arranger are both PRS members you should get 100% of PRS, split according to the split.