Because of the position of the fracture, the fragment of the tooth will be lost. A couple of alternatives are a root canal with crown lengthening, but my suggestion would be to remove the tooth and place an implant which will be a better alternative with a better prognosis.
Fractured lateral incisor
It is possible to remove the upper part of the fractured tooth and orthodontically extrude the root so that it could then have a post and core build up and a crown. This is, however, pretty heroic dentistry and it might not have the best prognosis. In the 21st century, an implant and a crown is a pretty successful option to consider.
I hope this has been helpful.
Douglas Jopling, DDS
Dall,as Texas area