A small rowan with hardly any berries: what is most likely to matter?

This looks like a common rowan, and I cannot see clear signs of disease. When a small rowan produces only a few clusters like this, it is usually because it flowered sparsely in spring or pollination was poor at the time.

The position probably plays a part. You describe partial shade, and the photograph shows a fairly wooded spot with competition from surrounding trees. Rowan can tolerate that, but less light usually means fewer flowers and therefore fewer berries. If the tree is still young, sparse fruiting is entirely normal too.

In early September, you cannot alter this year’s berry crop, so leave the tree undisturbed and watch its flowering next spring. To improve the chances of more berries, give the crown more light where possible by gently thinning competing scrub and small trees nearby, while avoiding hard pruning of the rowan itself. Watch particularly at flowering time: few flowers point mainly to shade and youth, while abundant flowers followed by few berries suggest weather during flowering, such as cold conditions or frosty nights.