The TDC Library has a digital collection online that includes admission and examination registers. Find them by searching for admission or examination at https://digitalcollections.tcd.ie/. There’s also a Printed Catalogue of Graduates of the university.
I got interested in this when researching my great-grandfather who was a graduate of TCD, but appears to have been in the Birmingham area during the time I would have expected he would be studying in Dublin. It turns out it was possible to get a TCD degree by being registered by passing an exam without studying there, that’s according to the book Trinity College, Dublin, 1592-1952 : an academic history, by R. B. McDowell, D. A. Webb, a copy of which is at Library and Archives Canada.