Msgr. Joseph R. Reilly will be Seton Hall University’s 22nd president, after a vote by the school’s Board of Trustees announced on Tuesday. As Reilly takes the helm of the private Catholic university in South Orange, his predecessor remains in court over the circumstances that led to his sudden departure in July. The school’s previous president, Joseph Nyre, sued the university in February, alleging that the school’s former board chair, as well as others, acted illegally and in violation of accreditation standards. Nyre has demanded reinstatement, back pay and benefits. Unlike Nyre, Reilly is …