They have a lot of cute gymnastics things that are personalized and inexpensive on etsy.com. I've been buying all of my daughter's teammates grip bags with their name and team name embrodiered on them on etsy. They are around $10.
DD got her big sis some cool nail polish and a gift card to Ulta beauty for her b-day, which was a big hit. For xmas last year she picked up some funky socks, a scarf, some headbands with the rubber inside so they stay put during gym, and a keychain with a pic of both of them and their names on it. Her big sis just turned 13.
PJ pants and fuzzy socks from Old Navy (cheap on sale)
foam and tape in bright colors
variety of small candies (if your DD meets her big sis, tell her to find out her favorite candy. fill a nice-ish plastic jar with A LOT of that one candy, and have your DD use sharpies to decorate the jar)
If you know nothing about the girl, when choosing colors use the team colors. I wouldn't do wristbands, as every gymnast has a brand and type they are particular to. Small gift cards are nice, but add in a trinket or candy so that the big sister can have something immediately, especially if she turns out to be younger than you thought.