Tactician's Gift is used to upgradeTactician instead of reinviting the Tactician.
Tactician's Gift can be obtained from Daly Quests, hunting monsters, EITCs, Notorious Pirates, Secret Missions, Monster Raid, and World Boss.
Depending on Tactician, different Gifts are needed for the upgrade. You can check the favorite Gifts of Tactician and required number for the upgrade in Manage Tacticians menu.
■ How to check the favorite Gifts of Tactician
Enter the game > Tap Jack Sparrow in your Territory > Manage > Tap Tactician > Upgrade