Formal:
* Perform: "The surgeon will perform the procedure."
* Execute: "The company will execute the planned procedure."
* Implement: "The school will implement a new procedure for attendance."
Informal:
* Do: "The doctor will do the procedure."
* Carry out: "The team will carry out the procedure."
* Go through: "We need to go through the safety procedure."
Specific to the type of procedure:
* Operate: "The surgeon will operate on the patient."
* Treat: "The doctor will treat the patient's condition."
* Repair: "The mechanic will repair the engine."
The best verb will depend on the specific situation and the level of formality required.