The client wants to appear more professional and polished. The current logo is too amateurish. They do like the idea of carrying over black, white and yellow to save some identity, but feel free to explore anything else that works. Also, they are not marries to the current font face (thank God!) or any attributes that you see here.
They were concerned about retaining some visual element of a comet, again to carry the brand over, but they think of it more of a spacey idea, and we're trying to push it more of a "clean" idea- like Comet will come in and clean sweep. So there is no need to make a literal "comet" in space or anything, but if you come up with something along those lines, great.
Also, this logo will need to work in a variety of environments: web site, biz cards, letterhead, envelopes, embroidered shirts, etc. So whatever you design should be able to be printed in 4 color, 2 color, greyscale, and embroidery. If this means a simpler, less detailed version for certain instances, that is OK.
The text on the logo should read "Comet Property Services"