So you are leaving to apply outside Canada? If your study permit expires during that time it is no longer valid. You cannot extending outland (as your title says) and don't expect it to take 4 weeks as doesn't include passport stamping.
What is your current status in Canada and when does it expire? Looks like you have been a student when did you stop studying and had you been studying full-time? Do you have PAL for the new program and when does the program start? What program are you applying for and at what school? What is your previous education and work history? Would also not count on 4 weeks processing depending on your location (what country). Also can’t count on approval these days?
