Create a dedicated exception, which has the appropriate abstraction level (something like UnstarTrackException). Throw such an exception, wrapping the original exception you caught. That way, the caller will only have to handle one exception (I assume all the exceptions should be handled the same way: retrying).
Whether this exception should be checked or not depends on your taste. If you want to force all the callers of your method to handle this exception, make it a checked exception. If you want to let the caller choose whether he wants to handle this exception or not, use a runtime exception.
If this method is buried deep inside layers of code, and if an exception can only be handled at the top layer, a runtime exception is probably a better choice. And in fact, unless you're the only caller of this method, a runtime exception is also probably a better choice. Checked exceptions tend not to be used much nowadays.