Eucalyptus gunnii

How do I cure the black spots?

Plant is possibly stressed, I wouldn't worry too much about the spots it could have been caused by the winter conditions or plant deficiency.  Feed with a general balanced fertiliser such as Fish Blood and Bone Meal or Vitax Q4, and hopefully it will grow healthier new leaves, once those shed plus make sure its well watered.But beware once they get going the growth rate is very fast and can dwarf a small garden within a few years, so prune like you would a Buddlia to keep shape and height.

@solly1961 thanks for the advice, I think I’ll keep it in a pot and try to create a bushy shrub.