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This would be a "prejudgment writ" or a "temporary restraining order" (a type of prejudgment relief).
The standard to get such an order is very high - the party asking for the relief must show that absent the court order they will suffer "irreparable injury", show that there is no lesser mechanism to prevent this injury, and show that they have a high probability of succeeding in the litigation.
If you want to pursue this kind of motion, I highly recommend retaining a lawyer, not only is the motion very difficult to prevail on (for the reasons I identified above), but these motions tend to have a significant amount of leverage for the remainder of the case (if you can prevail in getting a pre-judgment writ, you can often get enough leverage to force the other side to give you much greater concessions in negotiations (getting a pre-judgment writ can sometimes be enough to win the case).
As far as the actual procedure, these are usually presented in an "ex parte" motion, but depending on the specific facts of the case, the court may grant a temporary hold or stay from the time of the ex parte to allow the parties sufficient time to brief the motion for a noticed hearing.