Current members in expired membership search results
You don't say how many membership types you have, so I will assume that you only have one.

You could create one smart group (SG1) with criteria Membership status = expired and another (SG2) with membership status of new or current. (And perhaps Grace depending on whether you want those people excluded from your final smart group or not.)

Then you can use the custom search  Include / Exclude Search including SG1 and excluding SG2 to define a third smart group that you clearly label as the group to be used when ex-members are required.