Could a diocesan priest decide that he will only celebrate the TLM? Is he allowed to do so? What could a bishop do if he disagrees with the priest?
First, a diocesan priest could decide to say only the TLM. He would then have to live with the consequences. His bishop and/or the pastor to whom he is assigned as an assistant may not like that decision. The consequences would be nearly immediate.
So, Father says “YES!”, and the Bishop says, “NO!”
They go back and forth like this for a while.
In the end, Father has no real power to defend his decision. He might be right or he may be wrong, but he has no effective power.
If the Bishop were unhappy enough, he would probably suspend Father, take away his faculties to celebrate Mass publicly, preach, hear confessions, etc. He could move to remove him from his parish, if he is pastor. The Bishop could reassign him, if he is an assistant, to just about anything… or nothing. He could make Father’s life so awful that the he might want to leave the diocese or the priesthood.
The suspended or unassigned priest could appeal to Rome, but I’m 99.9% sure that he’d lose. Rome would back the Bishop.
On the other hand, a Bishop capable of thinking outside the box might say, “Okay, Father. We were thinking about closing old St. Eulampius over in Pie Town, but why don’t you have a go with your Latin and so forth.”
It all depends on the bishop. Some are open-minded. Some are not. Some are creative thinkers. Some are not. Some are good-natured. Some are not. Some are really concerned for the good of the priests. Some are not. All of them are at times and in different circumstances a combination of all these. They’re human, after all.
Most priests know where they would stand with their bishops on matters like these.