Is it permissible for a female Quran tutor to teach a female student Quran outside of the study circle and while awaiting the opening of registration?

What you wish to do is good and beautiful, because it falls under mutual cooperation in righteousness and piety, which is commanded in His (Allah's) saying, "And cooperate in righteousness and piety," and due to the Prophet's (peace be upon him) saying, "The best among you is he who learns the Quran and teaches it." You must be diligent in mastering what you learn.