Definitely agree with the 30-day quarantine.
Introducing birds should be a slow process, step by step. Once quarantine and avian checks have been completed, allow them to see each other. Then you can allow them out of their cages on separate play stands or separate perches. Do this for a few weeks.
The conure is likely a much larger and stronger bird than your cockatiel. His advanced age and smaller size puts him at risk for stress, which can cause heart issues in an elderly bird. Watch for panting or any signs of stress. If this occurs, immediately remove him from the situation. Sitting quietly in a dimly lit room for an hour can help calm him down.
If there are still no signs of aggression or stress, then you can begin moving them closer and closer. Again, patience is your friend here. They very well may bond and become close friends, but a slow pace is the best way to introduce them.
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