So I don't really ever enter the art challenge, and I'm sure you can obviously see why (I SUCK!). But this one gave me an idea, and although I am terrible at this I thought what the heck. Let's give it a shot.
The Starfleet delta has probably been seen all over the galaxy by pre-warp civilizations. So I went with the idea of one of those worlds turning it into a holy icon. I'm not sure I portrayed it well, but here goes...
I imagined this civilization using the delta itself as a backdrop, with something being placed over the top of it. They would use it's traditionally gold color, which many civilizations in our own past have given a sense of divine importance, including tying it to the sun. The lines at the cardinal points represent this as well, a very common way to depict the sun or various Gods.
The green area I added to give it a little more to look at. It's meant to be a rather simple representation of the Vulcan salute, but after hundreds of years of being redrawn and reinterpreted it doesn't look quite like the real thing. I also thought of paraphrasing the quote "The needs of the many outweigh the needs of the few, or the one." Their line, which they would use in much the same way we throw around "Do unto others," would be "That which helps the many is greater then that which helps the one."
So, yeah, that's it. Hope it's not too horrid.