All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
You should wait for the regular imaam as long as this would not entail delaying the prayer for long or cause harm or hardship on the congregation. This is because waiting for the regular imaam fosters unity and harmony among the people of the mosque. Indeed, whatever is essential to enable one to carry out an obligation is also obligatory. Moreover, the regular imaam has a right over the worshipers to wait for him if he has an excuse as long as waiting for him would not cause hardship, as has been mentioned above.
The regular imaam has the right that none takes his place in leading the prayer except with his permission, as the Prophet, sallallahu ‘alayhi wa sallam, said, "Do not lead a man in prayer in his house or where he has authority, and do not sit in his place of honor in his house, except if he gives you permission or with his permission." [Muslim]
However, if the regular imaam is late beyond what is customary according to the people of the mosque and they know that he will probably not come given their knowledge of him, then they may hold the congregational prayer and choose the worthiest of them to lead the prayer. The Prophet, sallallahu ‘alayhi wa sallam, said, "A man who is well versed in the Book of Allah and can recite it better is most worthy of leading the prayer; if (all those present) are equal in this respect, then the one who has most knowledge of the Sunnah; if they are equal in that respect too, then the one who made Hijrah (emigrated to Al-Madeenah) first; if they are equal in this respect too, then the one who embraced Islam first should lead the prayer." [Muslim]
It has been narrated that the Messenger of Allah, sallallahu ‘alayhi wa sallam, was late for the prayer time, and Abu Bakr, may Allah be pleased with him, led the prayer. [Maalik in Al-Muwatta'] The same thing happened during the Battle of Tabook. "He, sallallahu ‘alayhi wa sallam, was late for the congregational prayer, and ‘Abd Ar-Rahmaan ibn ‘Awf, may Allah be pleased with him, led the prayer. When the Prophet, sallallahu ‘alayhi wa sallam, arrived, he joined the prayer behind Ibn ‘Awf. When Ibn ‘Awf made Tasleem (ending the prayer with the Salaam), he (the Prophet) stood up and completed what he had missed (of the prayer)." [An-Nasaa'i and others; Al-Arnaa’oot and Al-Albaani graded it saheeh (sound)]
The fatwa of the Permanent Committee for Islamic Research and Fataawa reads, "The basic principle is that no one is permitted to lead others in the prayer in a mosque that has a regular appointed imaam, except with his permission. This imaam is the one most entitled to lead others in the prayer. However, If he comes later than usual, then another person may lead the people in his place in order to avoid difficulty."
Allah knows best.