You will need to ask HP if their bios supports the i7-2820QM.
In my opinion, it makes no sense to attempt to upgrade a laptop this old.
Doc (not an Intel employee or contractor)
[Windows 11 is the new Vista]
Due to this product being discontinued, Intel Customer Service no longer supports inquiries for it, I am glad to see that fellow community members have the knowledge and they jumped in and are helping you. You may also find the Discontinued Products website helpful to address your request.
You can verify this product's discontinuance status at the Intel
Please keep in mind that this thread will no longer be monitored by Intel. Thank you for your understanding.
Intel Customer Support Technician