Join in teaching, preferably with a nonacademic colleague, mathematically based specialty courses already offered in other departments. It seems inefficient and ill advised to allow a serious divergence between advanced mathematical applications and advanced mathematics. Create new mathematics courses focusing on the techniques most needed in certain applications, and include substantial course material on those applications. It is natural to share teaching in such courses with at least one other department and with nonacademic mathematicians. Develop general courses on industrial mathematics.
Several books are available that offer suggestions and guidelines.
Participate in or initiate programs in computational science, which stress a combination of mathematics, computer science, and applications. Existing computational science programs typically involve nonacademic scientists from several disciplines. Invite speakers from other disciplines, including scientists from industry, to speak in research seminars or colloquia. Such interdisciplinary gatherings can also be organized in cooperation with other departments. Maintain a departmental database, with links to national databases supported by government agencies, of summer positions or internships in industry or government laboratories.