Passport expiring during the school year, renewing during application process

[BlueVelka]

I'm applying for a student permit, and my school year lasts one year from August 2016-2017. My problem is that my passport is expiring October 2016, but I have applied for a renewal which is set for late may, but I fear I may miss my first day due to processing times. Is it possible/okay to apply with my expiring passport, and then renewing both my passport and permit at a later date? And if so, is there an optimal way to do it?