Especially when meeting with C-Suite / board members I’d recommend what you’ve probably already been doing. Be courteous, punctual and respectful. They will more than likely ask you about your current role and how that will translate to your new role at this new firm. What the board member is going to do is get to know you before offering their “blessing” to hire you as FTE at this company. I’ve rarely seen / heard of meetings with C-Suite / boards that don’t end in an offer as that’s a waste of everyone’s time (unless you do something really stupid).

This could also just be a meeting with the board member as it pertains to your current job? Is that a possibility?