Yes, this is very much possible to determine that she has a gene that has not been previously associated with xeroderma pigmentosum (XP).
XP is a heterogeneous genetic disorder. It is caused by any one of the genes involved in the process of nucleotide excision repair. Also we come across another protein involved in NHEJ through research on cell line 2BN. So it is always possible that this new patient has a mutation in a gene that has not been previously associated with XP and encodes a gene necessary for nucleotide excision repair.