What is the ruling on working at the Police Academy, given the presence of unpaid mediation, and knowing that the academy includes women who are immodestly dressed, and that working there requires shaving the beard?

If you are capable of fulfilling the responsibilities assigned to you, and you do not know anyone more deserving than you who was deprived of a job due to your intercession, then it is permissible to accept intercession. However, it is not permissible to work in a job that necessitates falling into forbidden acts, such as intermingling with immodestly dressed women and shaving the beard. Unless you are compelled to do this work to earn a living, or if abandoning college entry would lead to a greater harm, then it is permissible for you to accept the intercession, in order to commit the lesser of two evils.