Professor Parry is an academic and a qualified barrister. His research interests lie at the intersection of law, history and language, and especially in the context of Wales and the Welsh language. He has a sustained record of scholarly publications, including monographs, articles and contributions to edited collections. He has served on several national committees, in particular those concerned with the Welsh language, including the Welsh Language Commissioner's Advisory Panel, the Welsh Government's Welsh Language Partnership Council, and the Academic Board of Coleg Cymraeg Cenedlaethol.
He is a Fellow of the Royal Historical Society and a Fellow of the Learned Society of Wales