What is the evidence for the the necessity of waiting for the regular Imam for prayer, and what is the specified time for waiting for him?

The resident Imam has the first right to lead the prayer in the mosque, and he should be awaited as long as it does not cause hardship to the people. It has been narrated in the Hadith: "No man should lead another man in prayer in the latter's place of authority." So, if the Imam is late and it causes hardship to the congregants, or he is late beyond the usual time, it is permissible for someone else to step forward and lead the people in prayer, and the Imam should be advised against being late. As for the time between the Adhan and the Iqamah, there is no specific legal (Shari'i) determination for it; rather, it varies according to the circumstances of the congregants, and each mosque chooses the appropriate time for itself.