If you did a Celtic HS, you’d probably use standard gauge for it and run it from Edinburgh through Glasgow and Belfast to Dublin. Edinburgh-Glasgow-Belfast-Dublin is only about 400km. A French TGV train regularly does 320 km/h, so that trip would take less than two hours.
It would effectively turn Eastern Ireland and the Scottish Central Belt into one metropolis. Perhaps something that could finally compete with London.
It’s almost exactly the length of LGV Est (Paris-Strasbourg), which taken 1h50.
If Ireland reunifies and Scotland becomes an independent 🇪🇺 member state, this kind of project will potentially get a lot of financial support from Brussels.