The reconstruction of a disappear breed need to have conserved genetic materials , you can reconstruction extinct breed from its cryopreservation semen by repeat cross with one breed ( five generation will give you about 96.9% of the extinct breed ) , you can also reconstruction extinct breed by cryopreservation of embryo , the molecular approach also by bank gene .
A number of countries have germplasm repositories for livestock and plants. Frozen semen is one of the stored assets as well as some embryos. Certain lines of cattle have been restored from these resources. If the extinct breed disappeared in the last 60 years or so, then there may be stored semen available or at least semen from closely-related lines/breeds. If you are starting with DNA, it is a much more difficult process.