Conversation so far:
When did the reign of Gwynedd begin in Wales?
Maelgwn Gwynedd was king of Gwynedd during the early 6th century.
Who were the Britons fighting after the Romans left Britain?
The Britons were fighting invading Gaelic tribes from Ireland.
How did Britons' conquest of Wales over the Irish Gaelic tribes go?
Maelgwn Gwynedd's father Cadwallon Long-Hand completed the process by destroying the last Irish settlements on Anglesey.

Question: Who started the conquest?
Self-contained rewrite: Who started Britons' conquest of Wales over the Irish Gaelic tribes?