How can I follow up a delayed study permit application?
You can try to contact Immigration, Refugees and Citizenship (IRCC) through a number of different means such as by webform, email or through an MPs office. However, if you have exhausted all of the ways to follow up your delayed application, you may be able to compel IRCC to process your application by bringing an application for Mandamus in Federal Court.

Should I start a Mandamus Application in Federal Court? 
A Mandamus application in Federal Court is appropriate for cases that have been unreasonably delayed. This "unreasonable" delay is determined by looking at a number of factors including the type of application, the average processing time for similar applications and whether you have contributed to the delay. If your case is unreasonably delayed and your follow ups and requests for IRCC to finalize your application has not been adequately answered, then a Mandamus application in Federal Court may compel IRCC to finalize your application. 

What are the possible outcomes of a Mandamus Application for a delayed study permit?
A Mandamus application is an attempt to compel IRCC to finalize an application that is unreasonably delayed. The result of a successful Mandamus process is a requirement that IRCC proceed with finalizing its decision-making process. The Mandamus process does not impact the result of the decision-making process on your application but rather provides a timeframe for the finalizing of your delayed application. 
How long does a Mandamus Application Take?
Due to the staggering number of delayed immigration and citizenship applications, many Mandamus applications settle quickly after they start, and often applicants see results in the finalizing of their applications in 1 to 3 months. However, each application in court is unique and the processing time may differ if an application does not settle early and needs to proceed through the full process in court for a judge to determine whether leave will be granted and if yes, the outcome will be determined after a hearing takes place.