Remember that being a good GSA (speedweaving, backups, change requests, guests) is all expected. You are a GSTL and its assumed you will be a great GSA, just like a SFTL is assumed going to be good at all things a Salesfloor TM would do (zoning, pulls, setting SPs, PTM and Merchandising). Those things will make you a good GSA.
A GSTL is meant to focus on the team. It is one of the largest teams in the store, so the way you impact the group as a whole is most important. You need to put yourself into a parent-like position with them, where you hire them, train them, get to know them, and get them to make you proud. They should be invested in you and not want to quit because they enjoy working for you (not because you are their friend, but because you make their jobs better). You want to be the person who has them wrapped around your fingers, and you always push them in a positive direction (sometimes a GSTL will get there with their team, but get too gossipy with them). Always drive fairness and consistency and explain why you are doing what you are doing. You will be surprised what people attempt to make an issue (the drama talked about before), but if you knock it down and explain why your negative people will realize there is nobody who is going to listen to that kind of stuff.