In Assassin's Creed, the Templars are the secret order opposed to the Assassins.
The franchise presents the conflict as a long-running ideological struggle. The Assassins defend free will and resist centralized control, while the Templars seek peace through order and control over society. Their methods and goals are simplified and fictionalized for the series, though the names draw on historical traditions.
The rivalry stretches across many eras, from Altaïr's Crusades-era missions to modern-day conflicts involving Abstergo Industries. Different games use different local leaders, factions, and aliases, but the Templars remain the recurring opposing organization.
The Hidden Ones are the historical precursor organization to the later Assassins, first shown prominently in Assassin's Creed Origins. The Medjay are protectors in ancient Egypt, including Bayek, and the Borgias are a powerful family central to Assassin's Creed: Brotherhood. Those groups may oppose particular characters, but they are not the series-wide secret order opposed to the Assassins.