Relics are dropped in missions, some in sieges, other in daily quests and the arcane portal. As far as we can tell, in their category, the relic drops are random, while "normal" relics seem to drop more often than "purple" relics.

The Lords trait Treasure Hunter improves your chances of getting relics, as it generally improves chances to get chests from guards

From the awakening tab, in the relic details, it tells you where this specific relic can be found.