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Hi, yes, you can simply install Trezor Suite on the new laptop and start using it with your Trezor device.
The Trezor Suite on your old laptop cannot be used anyhow without having Trezor connected, as your physical Trezor is what has the private keys.
If you have your device “remembered” in Trezor Suite, it can only serve as a watch-only wallet, but no funds can be spent from there.