Mythic Odysseys of Theros doesn't include a way to apply its Piety rules to another pantheon. However, The Dungeon Master's Guide (page 23) does include a section on altering the Renown system to allow for measuring Piety, which is less fleshed out than in Theros but functions similarly.
Using this approach, you track renown based on specific divine figures in your campaign. Each character has the option to select a patron deity or pantheon with goals, doctrine, and taboos that you have created. Any renown he or she earns is called piety. A character gains gains piety for honoring his or her gods, fulfilling their commands, and respecting their taboos. A character loses piety for working against those gods, dishonoring them, defiling their temples, and foiling their aims.
The gods bestow favors on those who prove their devotion. With each rank of piety gained, a character can pray for divine favor once per day. This favor usually comes in the form of a cleric spell like bless. The favor often comes with a sign of the divine benefactor; for example, a character dedicated to Thor might receive a spell accompanied by the boom of thunder.
A high level of piety can also lead to a character gaining a more persistent benefit, in the form of a blessing or charm (see chapter 7, "Treasure," for such supernatural gifts).