I am upgrading my laptop's CPU, it has a sticker on it.
Should I leave it on and apply thermal paste ? Or should I leave it like that ?
I would take the sticker off. But it's not causing any issue. It looks like it's entirely below the level of the part of the CPU that makes contact with the heat sink.
To the best of my knowledge:
Intel or AMD do not place stickers on the actual CPU. Meaning, you likely purchased this CPU from a different seller who placed their own sticker on it for their use. Meaning, removing this sticker will not void a warranty or be useful for identification later.
Thermal paste needs to make contact with the heat spreader, not the sticker which would act as an insulator.
Take it off. Peel as much as you can as cleanly as you can. Be careful and use rubbing alcohol to completely remove the adhesive. Of course, be very careful to not damage any pins doing this.
That is up to you.
Leaving it there will not affect the functionality of the CPU and does not get in the way of the CPU die on which you apply the thermal paste.
There are no issues with it there, but I'd probably take it off. There is no use with it being there, unless you need it there for a reason or for future reference.
You can use Isopropyl Alcohol (IPA) to help remove it if you have any on hand and know how to handle it properly.
Power up, and enjoy.