You need to stick to something with the same overall parameters. So to have a higher sidewall, you'll need to reduce the wheel size down from 21".
This website shows the options: https://www.wheel-size.com/size/audi/a7/2013/
In summary, the options are:
255/45ZR18 99Y
8.5Jx18 ET32
5x112
2.4 / 2.1
235/55R17 99H
7Jx17 ET25
5x112
2.4 / 2.1
235/55ZR17 99Y
8Jx17 ET30
5x112
2.4 / 2.1
235/45R19 99V
8Jx19 ET26
5x112
2.4 / 2.2
255/40ZR19 100Y
8.5Jx19 ET32
5x112
2.4 / 2.2
255/40ZR19 100Y
9Jx19 ET32
5x112
2.4 / 2.2
265/35ZR20 99Y
9Jx20 ET37
5x112
2.4 / 2.2
275/30ZR21 98Y
9Jx21 ET35
5x112
2.6 / 2.3
My only query would be whether a smaller radius will fit over the brakes, but from your picture the brakes look normal sized so you should be able to drop all the way to the R17