My father swore by Dulux paint and used to spend hours in England cleaning and preparing the surface, he said it is the most important part of painting.
After many years painting the house and perimeter walls in Thailand I don't think that applies here, the paint they make here covers everything under it with no preparation, mold, dirt, discoloring, it covers everything and does not come through later even after many years.
We have three rai of land and painting the outside wall is like paining the forth bridge, on our first attempt at painting we jet washed and wire brushed all the dirt and mold off, but as we moved on didn't bother, result after many years later absolutely no difference at all. I have a theory that Thai paint is made specially to cover everything,
I usually use TOA, sometimes I thin it with a little water other times I don't bother. Buying paint at the home depot shops is more expensive than buying it at a specialized paint shop
Picture attached is of wife and sister painting outside wall after fifteen years, as it was a lite color originally and trees and grass grew up against it, it did not wear well.
No need for undercoat on existing paint, just match it and paint over it after removing any loose bits.
Its is easier if you use a roller on a proper steel pole, not one of the plastic ones, they bend and you cant get the pressure on the roller.
Match and buy the paint yourself, make a note of the paint number, date and get a blob of paint on the label, check the base they used A B or C this is the variable, then find someone to do the job for you if you want, we have the big climbing frames and the little frames also ladders, trucks and dozens of brushes and rollers etc so we always do it ourselves.