Electrician here
Its a fused spur, as others have stated - I would always advocate getting in a pro, but these are simple enough if you consider yourself competent and are confident in your understanding of wiring.
First turn off the mains supply, best to throw the main switch at the fuse box to be 100% sure it's off as I doubt you have testing equipment.
Remove the two screws and carefully pull forward the plate. You will see the three wires from the flex connected behind - remove them noting carefully which colour goes to which terminal. phone with a camera is your friend.
New fridge, cut off plug, strip outer insulation and inner insulation to match what was removed, and re-assemble exactly as before.
Turn on, should work fine.
Its a myth that the fuse in the plug protects the appliance, it protects the flex from overloading under a fault condition, on a fridge one would use a 13A brown fuse, the one in the plate should be fine.
I'd still advocate for a professional, as we would test the Zs (earth fault loop impedance) and circuit breaker tripping time as we don't take it for granted there is a good earth at the plate.
Problems can occur doing this kind of thing, nothing of concern to me, daily occurrences, for example the existing feed cables being loose and all falling out - but that can flummox a DIYer!
I would also add if you have solar, ensure that the solar supply is shut off, I've seen odd set ups where throwing the main switch does not turn off the solar, in which case every circuit breaker and the solar isolating switch need to be off.