Is it permissible to shave the beard in order to return to teaching if one's salary depends on it?

If leaving work due to the beard would lead to greater harms, such as being the sole provider for your family, or leading to your ruin or the ruin of those you support, then there is no impediment to trimming it or shaving it, committing the lesser of two harms. As for taking a salary without working, that is permissible because teaching is a form of hiring (ijarah (definition)), and a hired person is entitled to the wage if he makes himself available to the employer, even if there is no work or if the hiring party suspends him.