Hard to tell from the picture, but it looks climbable. Keep an eye out for the obvious signs of decay, limb attachments, or splitting, etc. But as others have mentioned, dead Elm is generally rock solid(for the first 1-2 years anyway). Here when they get DED, they are completely dead within 1 year of infection. The second year, the bark will completely fall of the entire tree. Even at this point, when they have just shed the bark, they are incredibly strong. We climb and rig them all the time.
Its after the 2nd year of being stone dead that you need to proceed with extreme caution.