Originally, each Relic Armor piece could be found in only one Dynamis zone, and for each job only one piece could be found in that zone. However, with the addition of the Dreamworld Dynamis areas, there are now multiple zones where the Relic Armor pieces may be found.
To upgrade your Relic Armor to Relic Armor +1, talk to Sagheera in Port Jeuno (J-8) near the Windurst Dock. She will offer to repair your worn Relic Armor and make it all shiny and new. To do so, you will need to bring her your relic armor, a ragged version of your armor and a crafting item. In addition, she will charge you a fee for her services in ancient currency.