I've got some ideas, hope this helps!
- Career Night/Networking Reception: Students get to meet alumnae involved in specific fields. A little dry but it can get the ball rolling.
- Can alumnae be invited to certain ceremonies? The collegiate chapter in my town invites the alumnae chapter to the Alumnae Initiation, as well as the Founders' Day Brunch.
Is the advisor involved in the Alumnae chapter? Perhaps she'll have some suggestions as well...
While I'm not an advisor (yet!), I've been involved in other things where I interact with college students. Women around this age are so eager to speak with women who are a little older, but not their moms or older sisters, about life after college. I think an event or two would spark interest and then it would flow a bit more naturally.