The student endorsement is updated once a year. Late stay endorsement can also be handled at China Travel Agency in Hongkong.
Of course, you must issue a Hong Kong identity card. Within 30 days after your arrival in Hong Kong, you can go to the Immigration Tower in Wan Chai with a Hong Kong and Macao Pass. It's free to apply for an ID card for the first time, and it will be ready in 14 days. The procedure is simple and no "application" is needed.
In fact, anyone (over 1 1) who is allowed to stay in Hong Kong for more than 180 days must apply for a Hong Kong identity card within 30 days after his arrival in Hong Kong.
You can apply for a Hong Kong permanent identity card if you have legally resided in Hong Kong for seven consecutive years. Four years in college. Work and study.