In the time period between the end of the Demonic Conflagration and the fall of the Punishing Star that sank much of Spartak, the Quaternity church had very little presence.
The church was in the forefront of the war against Demons and lost many clerics and paladins during the war so there was not a large force to recruit followers after the war. The church’s legions of worshippers had diminished because of the Quaternity Inquisition, which proved to be filled with corruption, even though the goal of the bloody Inquisition turned out to be sound: the rooting out of demon-possessed individuals which was a Pre-Cataclysm to the invasion which followed.
Another factor in the post-war decline of the Q-church was the story that the demonic rift which opened was the result of actions taken by a fallen Paladin, St. Kargoth. Many faithful felt the church could have prevented the terrible tragedy of the war.
And finally, the center of the Church’s power, the Tower of the High Clerist had been abandoned during a series of attacks during the war. The churches vast collection of holy relics and artifacts were scattered and hidden away from attempts by the Demons to destroy them.
So, while there wet still pockets of Quaternity worship tucked away in villages and small towns, the church had very little influence during this time until after the Punishing Star fell and a young cleric named Elistan, rose to prominence during the War of the Lance and re-opened the Tower of the High Clerist.