Easy peasy - lol.
Jack up rear wheel, remove wheel.
Push back existing caliper piston with screwdriver or other tool.
Clamp off flexi hose on caliper (don't crush it !).
remove flexi from caliper, remove caliper mounting bolts on carrier. Remove caliper, remove brake pads.
Replace carrier with new caliper & bleed after releasing flexi hose
Job done.
I’d probably look into replacing the flexi hoses or even the whole thing while you’re at it but then I do like a bit of overkill in the hope the car pays me back in reliability.
Asking about this in case there was something silly preventing easy change such as metal pipes on caliper.
I had unbolted them to clean them while pad changing, the pre MOT people said duff but they seemed OK to me, but been back, and they said binding when originally they said damaged.
I did the passenger rear one last year. Clamped the flexi pipe and then made sure the brake line would undo from the old caliper (got new banjo bolt in case it didn't) but left it on. Removed old caliper and hung it out of the way. Put new one on and then swopped the line over removed clamp and got my wife to operate the pedal while I bled it. Dead easy.
If you've clamped the flexibility on the rear before removing the caliper, you'll be fine to just bleed that corner. Brake fluid should be changed every couple of years because it's hydroscopic (excuse spelling maybe?) So wouldn't be a bad idea while you're messing with brakes anyway. Give the nipple a gentleish tap on top with a hammer. Helps if they're seized.
Not sure if we're able to comment on the state of your nipples!!!
However, I used a full hex socket with one of those sliding T bars to gently apply pressure and ensure the pressure wasn't off centre. Did the trick on mine.