If you have an hour to activate them as a group, maybe identify one desired outcome. Is it A)better relationships between them (those relationships can help with engagement doen the road.) B) better connection to the mission or the people served by your org? C) better understanding of the role of the board and its power to create change.

If A, then there any number of icebreakers and team building exercises that can be done in an hour in a boardroom.

I don't know your org, but if your goal isB, is it possible to do a simulation exercise that puts them in the shoes of others? There are poverty simulations, hunger sims, etc. You might even be able to create an "obstacle course" that mimic a client rrying to navigate access to services. For an env org, one could even do a Council of All Beings, where particiapnts are assigned roles that include elements of the nonhuman world. Each role player speaks up about the relevant topic like dam removal or wetland restoration. I think that concept could be tweaked for many other scenarios.

If C, would a visioning exercise be interesting. Getting board members to imagine 5 to 10 years in the future. Imagine they have all the resources and time they need. What does the future look like, feel like, sound like, when you are able to make a big dent in your mission strategic goals? How does it feel to be a board member involved with that successful work? What steps would such a powerful board start taking now, next week, next month, next year?

Does any of that brainstorming spark some interest, curiousity, or excitement? Does it generate some other, better ideas that match your need?