I am a state or local government agency lawyer. May I represent pro bono clients before judicial tribunals before which I do not appear as a part of my paid job?    

Yes, but out of an abundance of caution, you should ensure that all parties involved realize that you are acting solely in a personal capacity rather than in your official capacity on behalf of the government. As with all pro bono work by government lawyers, every step should be taken to check to make sure that such work is within the bounds of your agency or office’s pro bono policy.