Interestingly when our theology uses the term local church or particular church, it is not referring to the parish but the diocese or an equivalent structure. A pariah is a "community" or a "part" but it is never called "church." In our creed we proclaim a Church that is "one, holy, catholic, and apostolic." It is the bishop who in a unique way preserves the unity and apostolic nature of the Church. Without a bishop seven sacraments are not possible. Yes, if a diocese is without a bishop you can bring one in to ordain, but this is never to be seen as normal or normative. The norm remains that a bishop of a diocese should ordain priests and deacons who assist him in ministering to the people of the diocese.
In this time known as a vacant see that the Church calls priests to offer the mass "For the election of a pope or bishop." The word election can be confusing particularly because we do not in the modern sense elect or bishop. We use the word "election" because in Latin it refers not to ballots and votes but to choosing and being chosen. We use the word election in the same way in the RCIA. We pray for the 'election" and we will call him "bishop-elect" until he is installed, becuause he has been chosen, by the Pope and by the Holy Sprirt who we believe still guides the Church.
It is easy for any of us to slip into a very narrow vision of church, to see the diocese as merely bureaucracy. Perhaps in these days when we are without a bishop, it is not only a time for us to pray for the one who will be chosen, but also for us to deepen our understanding of what it means to be part of a diocese and what it means to have a bishop. Perphaps now would be a good time for all of us to read at least the first few paragraphs of Christus Dominus the Vatican II document on the role of a bishop. Jesus not only calls us to be individually disciples but we are called to be one Church.