Might be Carissa macrocarpa, Natal Plum. Does it bleed white latex when a leaf or stem is broken? A closeup photo of the leaves would help to confirm. Carissa macrocarpa - Wikipedia
Hi @Junglekeeper, Thanks for your response. Actually, it does not seem to bleed white latex when a leaf is broken. Here are some closeup photos of the leaves.
The growth looks like that of Carissa macrocarpa. I just removed an older leaf from my plant. There was some latex where the petiole attached to stem but almost none when I sliced the leaf in half as you did. I've noticed much latex in the past but perhaps that depends on the age of the leaf and the level of activity in the plant.
You are right, it might have something to do with the tree's age and/or activity. I will observe what happens this spring and wait for its flowers and fruits. Thanks again for your help!