OP, you really should just get a new receiver with Airplay built in. Wired is pretty much
always better than wireless.
AppleTV HDMI out into Receiver HDMI in, sending audio to all of the speakers you hook to the speaker terminals. You can also Airplay from Mac, iPhone and iPad to such receivers, as could guests you have over wanting you to hear the new song or watch the new video they want you to hear/see. Such a setup will allow you to add any other AV equip to the same system so that any other source can take full advantage of surround sound too, including AV equip that does NOT support Airplay.
If you want to build a "surround sound" system, that pretty much begs for at least 5.1 hookups for the 5 speakers plus maybe a good subwoofer. Having been building such systems for decades, I wouldn't even bother trying to do something like that completely wirelessly. In my experience, Airplay is really pretty good at STEREO.
See this for a bit more and several other quick searches seem to consistently suggest Airplay is limited to 2 channel stereo. More than 2 speakers starts begging for equip made for that... and for us consumers a great bit of equipment for that is a receiver, the central "hub" for all things AV. Even a modestly-priced one will deliver 5.1 well.
If you have some kind of absolute wiring obstacles for (getting wires to) the rear surrounds, perhaps consider some kind of hybrid setup with receiver wired to front left & right + center and wirelessly transmitting rear stuff to a sub (positioned
behind your seating area) to which rear speakers can connect. There are many 5.1 Soundbars that work this way. So you can probably find a way to do the same AND use the speakers you have.
There are also plenty of "hide the wires" options along floorboards, etc if you can't get into the attic or basement and/or are not already pre-wired for surround. Some of these are pretty flat, blend in well and are paintable to match wall colors.
Yes, you can probably find a simple amplifier with Airplay. Yes, you can certainly find something to use the wireless option. I'm less confident there is a hybrid, all-wireless option that will get you wireless (but full) surround sound 5.1 or 7.1 that also uses the speakers you have.
Bottom line: you'll cut all of the weaknesses of wireless (and walled garden) OUT by purchasing a new replacement receiver and using wired connections. Airplay to the receiver and it can then send the sound to all speakers you already have and those you may add in the future as you build out your system. IMO, it is the BEST way to go if you want
real surround with great flexibility for the future.
If you are asking for a specific receiver recommendation, that's much better for you to decide. Think about both your present and future needs. That should give you a sense of how many HDMI in ports you need. Obviously, you want one with Airplay. Think about your future speaker setup goal: is that 5 speakers + sub, 7 speakers + sub or more speakers for ATMOS? That will drive the number of terminals to seek on the back. Since the existing TV is "old", is the next TV going to be 4K or perhaps 8K? If so, be sure the receiver is capable of passing through whatever signals you think you'll want to pass years from now. Etc. In short: do some good research to find a few that best fit not just what you need now but what you'll probably want it to manage 3-5 or more years from now. A good receiver can be useful for upwards of 8 or 10+ years. But that only works out if you plan for what you'll prob want it to do in 8-10 years (too).
