UdeM’s steps for whole process: http://www.bei.umontreal.ca/bei/documents/Renouvellement_autorisation_ANGLAIS_Fev2016_revue_2.pdf
contact for CAQ people: 514 864-9191
https://www.quebec.ca/en/education/study-quebec/renewing-authorizations
The steps are the same as for your first application:
Here is where you apply for the new CAQ:
https://www.quebec.ca/en/education/study-quebec/temporary-selection-studies
After applying for the new CAQ, it should arrive in 20 days.
If you apply before your permit expires, you can continue to study under the same conditions as your current study permit until we make a decision. This only applies as long as you stay in Canada.