If you have an active PlayStation Plus subscription (yes, it still works on PS3 in 2025), this is the easiest path.
On the PS3 XMB, navigate to Game > Saved Data Utility (PS3™) . gran turismo 6 save data ps3
: Check if you're using any cloud save services compatible with PS3 and Gran Turismo 6, as these can offer additional backup options. If you have an active PlayStation Plus subscription