Trust Master is one of the features of the game that rewards players with special items for achieving 100% with any given unit. Each unit has its own Trust Master rewards that can be increased in the following ways:

Quests: You will have a chance to gain 0.1% TM randomly after every battle.
Fusion: Enhancing your character with the same unit will guarantee a 5% TM increase. (e.g. The material unit's current TM% +5% will be transferred to the base unit)
Trust Moogles: Fusing this to your base unit will increase its TM% depending on the Trust Moogle's rarity (e.g. 1★ Trust Moogles provide +1%, 3★ Trust Moogles provide +5% to matching TMs, 4★ Trust Moogles provide +5%, and 5★ Trust Moogles provide +10%)

You will receive a unit's reward once it has reached 100% trust mastery.