Is it permissible for a female student to pray Dhuhr at its early time before the delayed adhan in her place of residence, especially since she continues studying after Asr?

The validity of prayer is conditioned upon the entry of its time. So, if the time for Dhuhr prayer has begun, and the muezzin has not yet called the adhan, you are permitted to pray. However, if you pray before its time, your prayer is invalid. In the event that the lesson continues until Asr time, and you know that you will be prevented from praying, it is permissible for you to intend to combine Dhuhr and Asr prayers by delaying them until after the lesson concludes. Scholars have permitted combining two prayers in cases of hardship, due to the general texts of Sharia that indicate ease and the removal of difficulty. However, this concession should not be taken as a regular practice.