We had the exact same gap—home at 4, bed at 9, five hours of "what now?"
What didn't work: banning screens entirely. Created a battle every night. I was exhausted, she was resentful, nobody won.
What worked: we use AirDroid to set a hard cutoff at 7pm. Not my rule—"our rule." We agreed on it together, and the app just enforces it so I'm not the villain. 7pm hits, her tablet locks. No negotiation, no "five more minutes."
Before 7pm, she has free screen time. After 7pm, it's "protected time." Board games, cooking, audio books, Lego, whatever. Honestly sometimes she just lies on the floor complaining for 20 minutes. That's fine. The boredom passes.
The trick was having the cutoff be automatic. When I was the one saying "turn it off," it was personal. When the device just locks, it's physics. She can be mad at the device. I'm just there with snacks.
Also: we started the 7pm rule on a Friday, not a school night. Less pressure, easier to stick.