If I already have an open position with 10x leverage on a contract, for example BTCUSDT-PERP, and then I want to open another position on BTCUSDT-PERP with 15x leverage, what will happen to my open 10x leverage position?

The display on the cross margin of an open position at 10x leverage will change to 15x leverage, and if your margin balance is sufficient, the previous open order will continue to run at 15x leverage with the amount of initial margin required adjusted to your leverage level.

The only change is the entry margin display in the app for calculating subsequent additional positions. If you add a position, the initial margin will be calculated based on the newly selected leverage.