If you don't use web3 exchanges that support web3 wallets, you can not connect your hardware wallet to that exchange and trade or do anything else directly.

You only can send your btc or etc from that hardware wallet to an address on your account in that exchange, and wait for the exchange to credit your deposit to your account. After that, you can start trading on that exchange, and withdraw your cryptocurrency out of it if you want, and if that exchange does not scam you.

Reminder: do not keep your money in online accounts.