Academy Loremaster
Creature — Human Wizard
At the beginning of each player's draw step, that player may draw an additional card. If they do, spells they cast this turn cost 
more to cast.
As a young student, she dusted the shelves of Tolaria's great library. Now, she writes the books that line them.
Marcela Medeiros
Dominaria United (DMU)
• #40Rulings
The cost increase applies to spells that player casts even if they're casting them for an alternative cost. If they cast a spell without paying its mana cost, they'll still have to pay {2}.
(wotc • 2022-09-09)
Abilities that reduce the cost to cast a spell apply after abilities that raise them. For example, if an opponent chose to draw an additional card as Academy Loremaster's triggered ability resolved, Argivian Phalanx (a card with mana cost {5}{W} and the ability "This spell costs {1} less to cast for each creature you control.") will cost them {W} to cast that turn if they have seven or more creatures.
(wotc • 2022-09-09)
Rulings
The cost increase applies to spells that player casts even if they're casting them for an alternative cost. If they cast a spell without paying its mana cost, they'll still have to pay {2}.
(wotc • 2022-09-09)
Abilities that reduce the cost to cast a spell apply after abilities that raise them. For example, if an opponent chose to draw an additional card as Academy Loremaster's triggered ability resolved, Argivian Phalanx (a card with mana cost {5}{W} and the ability "This spell costs {1} less to cast for each creature you control.") will cost them {W} to cast that turn if they have seven or more creatures.
(wotc • 2022-09-09)