This is not normal behavior. First things first. Make sure that you had a female and not another male. Usually, females are not as aggressive as the males and will not facilitate a chase. If anything, a male will chase a female, but will usually not hurt her unless she is extremely young. If you do have a female, then she may not be ready to accept the new male (too early) and the new bird (if it is a male-again make sure what you have) may be too young and intimidated.

The best procedure would be to place the new bird in a pen (half in the water and half on the bank with a feeder in the pen). Keep him in the pen for about 2 weeks, giving both swans time to acclimate to each other. Once you release him, constantly monitor him for signs of aggression from either swan. If there is any sign of aggression, this mating is not going to work so you will need to find the new swan a new home. If the "female" is not willing to accept this new bird, it is unlikely she will try to accept any other bird so it would be futile in trying to find a mate for her. Good Luck. The Regal Swan