Kathleen, I am wondering if building trust is akin to succession planning. Incoming leaders usually commit to listening and learning and benefitting from institutional memory. Leaders about to exit not only encourage organizations to remain true to their principles but also ensure the record of joint accomplishments carries on to inspire future members of the organization. Trust relies as you have pointed out on open communication and shared values. I wonder if that is not accomplished by a historical perspective: self and organization evolve. With the long view, change is possible. The possibility of change builds trust because a it-might-be-otherwise view leaves room for coming-together. At least it provides a ground for alternative stories. Of course, good institutional memory rests on excellent record keeping. Trust is not just about commitment to those we engage face to face but also those that come before and are to come after. A leader should be able to articulate that in a meaningful fashion.
I hope this helps a little and sparks the elaboration you are seeking,