Replacement Graphics card

Since your Mac is obsolete (Obtaining service for your Apple product after an expired warranty - Apple Support), any repairs would not be done with Apple genuine parts, and you certainly don't want that!

As your MacBook Pro is old, it is best to replace it. Your Mac has not received a software upgrade for quite some time and therefore is not as secure, it is no longer supported, and any other component could fail at any moment.

Here is the current Mac product lineup: Mac - Apple.

Apple also has refurbished Mac computers: Refurbished Mac - Apple.

Cheers,

Jack

I could have sworn another reply from me was posted, but ... so try again ...

I upgraded to a 2019 to keep my 2011 that can still perform usable SL-capable tasks working. Your old warhorse apparently served you well.

To reuse information on your old system use this enclosure https://eshop.macsales.com/item/OWC/MOTGS3U3/ from OWC after you extract the old HDD/SSD. OWC can help you with instructions to extract it. Use the enclosure in the future to swap any number of backup drives.

If there is still service (5 year limit) they replace the logicboard. If the system has a soldered-on SSD (touchbar model) you must backup the SSD before you replace the board.