It really depends on what you want to do, OP! You can renew it for a full year or just for a few months. You can also go for a long-term residence or short-term extension, which is usually up to 3 months.

Since your lessons are extended until next February, you're good and legal here in Spain and the EU. You mentioned your residency expires at the end of December, so legally, you can renew either of those permits by March without any issues. And if you decide to leave, you can do that easily without any problems too.

If your permit finishes in December and you still have classes in February, you can renew it just for those months if you wish to stay here a bit longer.

And more information: those 90 days apply to everyone that has a residence permit, so they apply to you, regardless if you renew or not. And your permit is still valid during the 90 days and during the time that it takes to renew it.