Oh yes! Relevant valve test procedures according to the plant or local authorities or end user, which again should refer to the international recognized authorities standard tests.
Also relevant for fluid application type and pressure. Emissions through stem sealings?
Even if the valves are produced to the API requirements local end users could require tests according to other standards, depending where you are in the world.
If tested mounted in pipelines other procedures may prevail.
If you are the buyer, buy valves already factory tested, and if overhaul include tests in your inquiry / specification for overhaul.