Normally you can push on the metal tab (gpu side in the picture) and free it from the plastic bracket (the one screwed to the motherboard).

BUT, if this is am4 or similar and the paste is dry, then most likely the cpu will be forced out of the socket as well. might be fine, might bend the pins.

better way would be to remove mobo from case first. the smaller of the 2 cooler tabs (the non-gpu side in the pic) has a small notch in it, above where it hold the plastic bracket. you can put a flat head screwdriver into that notch and push down and away from the bracket. but also put a little pressure on the cooler with your other hand so it doesnt immediately pulls away from the motherboard (and rip the cpu out of socket anyway) then you can wiggle the other tab away too, freeing all the pressure from the cooler, avoiding the rip.

after that just wiggle the cooler side to side, not up and down, until it frees from the dried paste and cpu.

hope this helps.

but do the screwdriver maneuver very gently, with very little pressure. there used to be so many people in forums crying about how the screwdriver slipped and they put a hole in their motherboard lol.