Magisters are the wealthy and powerful of the Free Cities, which given the nature of the Free Cities’ economies overwhelmingly means merchants:
The true authority [of Lorath] resides with a council of magisters made up of nobles, priests, and merchants. Its isolation meant that the Lorathi were little involved in the events of the Century of Blood, save for those few who sold their swords to Braavos or Norvos.
[The Three Daughters] are mercantile cities, protected by high walls and hired sellswords, dominated by wealth rather than birth, cities where trade is considered a more honorable profession than arms. Lys and Myr are ruled by conclaves of magisters, chosen from amongst the wealthiest and noblest men of the city; Tyrosh is governed by an archon, selected from amongst the members of a similar conclave…
Her father, Lysandro Rogare, was the head of a wealthy banking family whose power waxed even greater following the alliance to the Targaryens. Lysandro assumed the style of First Magister for Life, and men spoke of him as Lysandro the Magnificent….Lysandro’s heir, Lysaro, spent vast sums in pursuit of power and fell afoul of the other magisters….