It's not a clear photo, but I think you are enquiring about the Lichen on the branches/twigs? A sign that your plant is possibly in a damp and still environment. It's not unusual for shrubs and trees to have this. Especially, older plants that are quite slow growing.
Sometimes, it is a sign that the plant is lacking in vigour. If you had good leaf growth through the growing season and healthy crop of plums, then it's not anything to be concerned with. But if you have not, then it's time to look at making sure your tree is happy. Drainage, enough sunlight and branches regularly checked pruned where necessary.
The young shoots look quite healthy. And of course the leaves are in the process of closing down for winter (assuming you're in UK or similar!) so you'd expect them to look a bit manky.
If that's a green twist tie in photo 2, I'd remove it. It's so easy to forget them - and then the tree expands, & the twist tie digs in to the bark.
Lichen grows when the air is unpolluted and so is nothing to worry about.