I planted 4 young hornbeam (Carpinus betulus) trees in my garden,
approx 4 months ago. I noticed several weeks ago a sticky surface on
the leaves, which is now dry, but the leaves have what appear to be a
sooty black mould covering them. The leaves are not dropping, but it
looks unsightly, and im concerned it may affect the trees in the
future. When it rains it washes some of the mould off, but then it
reappears, any ideas ?

The "sticky stuff" is honeydew,the excrement produced by aphids. Sooty mold
grows on honeydew. It will not impact the health of the tree but the aphids
may. You can hose them off with a strong stream of water. Repeated aphid
infestations may require the use of a pesticide.
sed5555