My mother planted one of these in the 1950s. In those days it was classified in the Eugenia family as Eugenia smithii. Later it was renamed Acmena smithii and it's now classified as Syzygium smithii. It's reasonably common in older gardens around Adelaide, recognizable by its purple edible (but quite tasteless) berries.
The particular plant in the photo was one I grew from seed some years ago. It's one of many planted along a fence line but this one must be just far enough away to not get continually "pruned" by the ring-tail possums which love the new leaves of many Myrtaceae.
There are now many Syzygium cultivars sold in nurseries and this particular variety seems to have fallen out of favour but it's an attractive dense tree that holds its foliage almost down to ground level. It can be slow growing but eventually it reaches to about 4 or 5 metres although it can be trimmed and grown as a large hedge which can look quite stunning with coppery new growth like this in Spring.