installation lightroom/photoshop

yes, you can install it on your new computer. install the cc desktop app from here https://creativecloud.adobe.com/apps/all/desktop?action=install&source=apps&productId=creative-cloud and use it to install your adobe subscription and trial programs. 

you do not need to uninstall anything adobe from your old laptop, but you can and it won't affect the installation on your new computer.

I suppose you have the Photography Plan? You can install the software on as many machines as you want, but you can only activate on two machines. If you start the software on a third machine, you get asked to deactivate one of the two other machines. BTW: The mobile iOS or Android devices don't count in this, only desktop and laptop machines running Windows or macOS. You can mix OSs, having one activation on Windows the other on macOS.

https://helpx.adobe.com/download-install/using/install-apps-number-of-computers.html

[Moderator moved from Using the Community forums to Download & Install.]

1. Make sure your computer meets the minimum CPU & GPU requirements. Most Creative Cloud apps work on:

• Windows 11 (64-bit), Windows 10 versions 21H2, 21H1, 20H2, 2004, and 1909 (LTSB branches are not supported;)
• macOS 12 (Monterey), macOS 11 (Big Sur), macOS 10.16 or 10.15 (Catalina).

- https://helpx.adobe.com/creative-cloud/system-requirements.html
- https://helpx.adobe.com/photoshop/system-requirements.html
- https://helpx.adobe.com/photoshop/kb/photoshop-cc-gpu-card-faq.html

2. You can deactivate unused devices by logging-in to your online account.

https://account.adobe.com/activated-devices

Hope that helps.