I would say you can't have a trans-sex member of a single-sex species.
To be trans-sex is to change from one sex to another. This isn't possible if there is only one sex. Harpies, we'll use those since they are social, probably don't even have a concept of sexes in the way we think of them.
Now, What you might be able to do is create a new sex that mimics the role that other species play. In this case, I think it would be seen as becoming, at least in part, another species. Because that's what performs that role. Other species, not other members of the species. How harpies would take a Trans-harpy? No idea, but probably not very well.
At this time it isn't possible to be truly change sex in the real world, but we can come pretty close. Hormone therapies, surgeries, etc relate to this.
This brings us to gender. Genders are social constructs that center around biological sex. Sex is what your body is. Gender is what you and the rest of the world think that particular body means.
Changing genders is possible. You and society just have to agree that you are are no longer one and are now the other. In practice it's pretty messy, but the core is simple.
Now what this means for single-sex species that rely on other species to reproduce... who knows? Do harpies even have genders? Perhaps gender centers around whether a harpy has reproduced? Those that do are one, those that don't are another?