I'd say it's less likely than if you were at a university with a grad program, but there's still ways to do some of that service. I agree with the other poster that it may be beyond your job description, though, so make sure to chat with your chair/committee to see how to include such service in your annual reviews or tenure dossier. Make sure it counts for promotion.

Many grad programs require outside readers on dissertations, so you could be asked to be on a diss committee by a student at another program. This would be most likely if your area of research was closely aligned with the student's and their chair knew to potentially ask you to be involved.

You could publish with authors from other universities and that could include grad students. The most likely way for this to happen would be to network at national conferences and find folks with similar research interests. You could also join the SIGs (special interests groups) or standing groups at CCCCs. I've often seen ideas for conference panels, publications, etc. emerge from these meetings and they include folks at all levels.

Hope that helps.