Was the power to cast out demons given to anyone other than apostles?
Jesus listed the ability to cast out demons as one of the miraculous signs the early Christians would be able to perform (Mk. 16:17). While casting out demons is not listed specifically among the miraculous spiritual gifts Paul spoke of (1 Cor. 12:4-11), it would generically be included when he spoke of the spiritual gift which is “the working of miracles” (v. 10).
Not all early Christians could work miracles (1 Cor. 12:29), and not all had the same miraculous spiritual gifts (1 Cor. 12:29-30; 14:1ff). However, even though I cannot recall the Bible recording a specific instance in which anyone other than the apostles cast out demons, it is clear from the above passages that some in the early church in addition to the apostles could do so.