I too was 15 when my little sister (my only sister) was 7. She was a very girly girl and like to play dress up and pretend she was a princess or a mom (with her dolls being her children) or a teacher (with her stuffed animals and dolls being her students). I remember playing school with her. She'd be the teacher and I would be the "students," using different voices as I pretended I was the teddy bear student or the Barbie student or the camel student. We had a small chalkboard that she would write on to teach us the alphabet and nouns/verbs/adjectives -- whatever she was learning in school herself. She would ask questions after she read us a story.
I taught her games like "Rock, Paper, Scissors," and we played War and Memory with a deck of playing cards. I would put evenly-spaced dots on a sheet of paper, and we took turns connecting them to eventually make squares, like this --
Dots and Boxes - Wikipedia, the free encyclopedia. And ask HER what she would like to do -- even playing catch outdoors or identifying trees (maybe using a library book as a guide). And just do some storytelling -- "Once there was a beautiful princess named ....... who lived in ........" and so on (use lots of body language and appropriate facial expressions), letting your sister fill in the details as you tell the made-up story.