The sticky substance on your new fruit tree's leaves is almost certainly the work of common fruit tree pests. While this sticky substance is not dangerous, if left on the tree it can grow sooty mold which will impair the leaves' ability to absorb carbon dioxide and light. To remove the sticky substance, simply spray the tree's leaves with water. However, it is likely to come back unless you tackle the underlying infestation.
Brown Soft Scale
The brown soft scale is a small, immobile insect that looks like a crusty bump or scab on the tree's leaves. However, unlike bumps, they can be easily brushed off. Adult scales suck sap from the tree's leaves and then secrete sticky honeydew onto the leaves. To get rid of scales, spray the tree with a fruit tree safe insecticidal soap or horticultural oil in spring or early summer.
Adult whiteflies lay their eggs on the underside of leaves. And when the larvae hatch, they suck sap from the leaves and release ample amounts of sticky honeydew. In significant infestations, it can even be seen dripping from the tree's leaves. To get rid of the invaders, spray your fruit tree with a fruit tree safe organic insecticide as soon as you identify the whitefly's larvae.
Aphids are another fruit tree predator that sucks the sap from the tree's leaves and leaves behind a sticky honeydew residue that can be seen dripping from the leaves if present in significant amounts. Other signs of aphids are puckered marks and yellowed, twisted leaves. To control aphids, spray the undersides of the leaves with a fruit tree safe organic pesticide or insecticidal soap. Only spray the areas where you notice the infestation.
Other Sap-Sucking Insects
Other honeydew leaving insects like mealybugs, pear psylla and leafhoppers can be harder to distinguish by the damage that they leave behind. To properly identify the culprit, take a few leaves (and any insects that you can catch) to your local nursery to have them identified. Then ask how best to handle the infestation, but note that almost all of these insects can be killed with a fruit tree safe dormant oil or insecticidal soap spray applied to the tops and undersides of the leaves.