@Noob_liam 

What is the operating system of your hp computer? 

Please go to computer management-device manager-network adapter page to verify whether you can find the TP-Link adapter.

And please double click it and tell us the current device status. 

Try to go to program page to ensure that the driver has been uninstalled and try to reinstall the driver from official website. 

Good day.

@Noob_liam 

Below is the download link of the driver for Archer T2U.

https://www.tp-link.com/support/download/archer-t2u/#Driver

Note: Please verify the hardware version first. 

And if the network adapter does not show up under device manager page, try to change another USB port to plug it and verify whether there is any device disappeared and re-appreared during you unplug it and plug it back. 

Besides, try to change another computer to give it a go, if it still cannot be recoginized, you can contact the retailer or the local tech support to check the warranty policy. 

Good day.