Students are not required to apply for a new study permit if they change their field of study or switch educational institutions within Canada as long as their study permit does not specify this information. If the study permit specifies the institution or field of study then this information must be updated on the permit before the student can join a new course or school.
If a student changes their level of education, for example moving from primary school to high school, or from high school to university, then this would require modification of the study permit.
If you have applied to an institution in the province of Quebec, you must first verify that the level of study of the new program you wish to pursue matches the one authorized in your CAQ. If it does not, you will need to apply for a new CAQ.