Let's say I have a species similar to human, as sort of New Humanity. The only thing that separates them from humanity is their subspecies: the Sublorans. They have multiple animalistic features that separate them from the other subspecies. Most of the features that separate them are easily explained except for one: tails. As far as I am aware, there exists no species where one subspecies has a tail and another does not. Could a subspecies with this biological trait exist while the other lacks it? What evolution would support it? If so, how could it?
There is nothing strange or unusual about either having or not having a tail, It's just another anatomical feature which may be more or less useful for its survival. What makes a subspecies is that it has anatomical features or structures different from the species proper. The presence or absence of a tail would qualify. Subspecies can be interbreed which the tailed and non-tailed members of the two subspecies can have offspring who may or may not be tailed depending on the sort of genes involved.
If your tailed subspecies arose through normal human evolution it can be expected they arose from the same common ancestor out of which Homo sapiens sapiens (us) and Neanderthals sprang. This would be roughly one hundred thousand years ago or possibly earlier if subspeciation occurred before that. The Neanderthals later vanished. This leaves modern humanity and its tailed subspecies as the prevailing hominids on the planet. This is nothing but normal evolution in action.
Humans are one of the thirteen or so primate species and there is wide range of differences between primates. Chimpanzees and monkeys have tails. Gorillas do not. I have assumed the tails aren't that big, but size isn't the question. A tail might simply be a differentiating feature of a subspecies. There is absolutely no special reason why it exists. Sure sexual selection might play a role. That drove the evolution of the male peacock's magnificent tail. An explanation, evolutionary or otherwise, is not required for a tailed human subspecies.
One aspect of your question puzzles me considerably. You refer to a New Humanity and at the same time there is a tailed subspecies. I'm not sure if the tailed subspecies, the Sublorans, are a subspecies of the New Humanity or they are just a subspecies of human beings and they evolved alongside our human evolution.
If your New Humanity is truly new, namely, that it arose, say, recently, then how it arose recently will a major impact on what was responsible for having a tailed subspecies of the human species. For example, if this New Humanity was produced by genetic engineering, then its tailed subspecies could be nothing more than having the genes for a tail reactivated as a side-effect of the genetic engineering to create New Humanity.
Humans are (rarely) born with tails See this medical paper. The tails are usually surgically removed. So if your Sublorans possess a mutation that means tails are much more common than they are in the real world, and a culture which doesn't want those tails to be surgically removed, then yes it is quite possible.
The tails mentioned above don't do anything. They are not like the tails of Old World Monkeys and lemurs (used for balance) or like the tails of New World Monkeys (prehensile and used as an extra limb when climbing). If you want your tail to be functional rather than 'decorative' I think you'll have to handwave some genetic engineering into your Sublorans' ancestors.