Do the new rules make it possible for live beaver relocation?
Read this. I don't believe being a WCO gives you any exception to the law.
You can apply and get a permit to relocate wildlife. I bolded the relevent parts.
RCW 77.15.250
Unlawful release of fish, shellfish, or wildlife — penalty — unlawful release of deleterious exotic wildlife — penalty.
(1)(a)
A person is guilty of unlawfully releasing, planting, or placing fish, shellfish, or wildlife if the person knowingly releases, plants, or places live fish, shellfish, wildlife, or aquatic plants within the state, and the fish, shellfish, or wildlife have not been classified as deleterious wildlife. This subsection does not apply to a release of game fish into private waters for which a game fish stocking permit has been obtained, or the planting of fish or shellfish by permit of the commission.
(b) A violation of this subsection is a gross misdemeanor. In addition, the department shall order the person to pay all costs the department incurred in capturing, killing, or controlling the fish, shellfish, aquatic plants, or wildlife released or its progeny. This does not affect the existing authority of the department to bring a separate civil action to recover costs of capturing, killing, controlling the fish, shellfish, aquatic plants, or wildlife released or their progeny, or restoration of habitat necessitated by the unlawful release.
(2)(a) A person is guilty of unlawful release of deleterious exotic wildlife if the person knowingly releases, plants, or places live fish, shellfish, or wildlife within the state and such fish, shellfish, or wildlife has been classified as deleterious exotic wildlife by rule of the commission.
(b) A violation of this subsection is a class C felony. In addition, the department shall also order the person to pay all costs the department incurred in capturing, killing, or controlling the fish, shellfish, or wildlife released or its progeny. This does not affect the existing authority of the department to bring a separate civil action to recover costs of capturing, killing, controlling the fish, shellfish, or wildlife released or their progeny, or restoration of habitat necessitated by the unlawful release.
Here is the relevent part about getting the permit to release wildlife, beaver included.
WAC 232-12-271 Agency filings affecting this section
Criteria for planting aquatic plants and releasing wildlife.
(1) Release by persons other than the director. It is unlawful for persons other than the director to plant aquatic plants or release any species, subspecies, or hybrids of animals which do not already exist in the wild in Washington.
If such species, subspecies, or hybrid does already exist in the wild in Washington, it may be released within its established range by persons other than the director, but only after obtaining a permit from the director. (a)
Application for a permit must be made on a form provided by the department. It must be submitted at least thirty days prior to acquisition of the wildlife or aquatic plants intended for release or planting, and must provide all information indicated.