If the Cardinal wanted him dead, he could have attacked him the moment they entered the Northern Continent. However, the Cardinal's actions suggested otherwise.
Eren understood that the Cardinal's plan was not as simple as just killing him. The reason he brought Eren here and allowed him to witness the gruesome ending of the Demon Sect members was for a single purpose.
The Cardinal wanted Eren to feel hatred towards the Northerners. The Elders of the Demon Sect were known for taking revenge, even for the slightest of grievances.
The Cardinal expected Eren to go berserk and attack the Major Families of the Demon Sect that ruled over this area, ultimately leading to his death at the hands of the Necromancer Tower.
This way, the Cardinal could establish an undeniable grudge between the Necromancer Tower and the Demon Sect.
