Yes, Dough Bros are in there now. The Patrician Bros were trying to get their foot in there for years but their pizza was terrible and they could never make a go of it.

The story of the Pro-cathedral is fascinating. The foundation stone was laid in 1816 and it began competing at the amateur level in 1821. The cathedral went Pro just four years after it was built, ultimately taking on and defeating Nîmes Cathedral in 1825 to win the Cathedral Cup. It had little success for the next 100+ years after that as newer and heavier cathedrals came into prominence. Ultimately, the Pro-cathedral was deconsecrated in 1965 and reduced back to amateur status. The "New Cathedral" was consecrated that same year but, unfortunately, was built too late to turn Pro and compete in the Cathedral Cup (the Cup having been suspended during WWII and afterward labeled "undignified" and quietly let fade into history).

Galway’s Pro-Cathedral, a building of some significance
https://www.advertiser.ie/galway/article/119111/galways-pro-cathedral-a-building-of-some-significance#

Cathedral of Our Lady Assumed into Heaven and St Nicholas, Galway
https://en.wikipedia.org/wiki/Cathedral_of_Our_Lady_Assumed_into_Heaven_and_St_Nicholas,_Galway