What is the ruling on a woman uncovering her face and ears for a photograph in order to obtain residency in a non-Islamic country?

The ears and face are part of a woman's awrah (private parts) according to the consensus of jurists. It is not permissible for your wife to uncover them in front of a non-mahram for photography, except in cases of genuine necessity, such as traveling to reside in a non-Muslim country.