You're not technically a supervisor, the GSTL is. The GSA is typically the GSTL's *****. However when there isn't a GSTL around most stores hand control over to the GSA. You can "request" tasks of people, and help with training, but in NO WAY can you coach somebody. Ever. GSAs aren't TLs nor are they expected to in any capacity (except their task workload), so you're limited in the amount of "leadership" you can execute.
What to expect? You can expect that the entire Front End workload is going to be dumped on your shoulders, if you're lucky, your GSTL/GSA team will all pitch in equally.
I recommend going to the Guest Service section of the guides forum and read all of the applicable work areas for guest service.
Welcome!
EDIT: Also it varies from store to store. Some stores use GSAs as GSTLs on the cheap and expect more leadership (whilst receiving the same pay), while other stores use GSAs for Cashier/Guest Service/Cash Office primarily, and a backup GSTL.