Hard to see the photo clearly enough, but it looks like you have most of what you need.
Would need to know what frequency your agency uses and the full model number of your radio to know if it's compatible.
You'll also need a properly installed and tuned antenna.
I'll also add this just so you are aware, I'm not the radio police, just passing this on since many are unaware.
You, as an employee, volunteer, etc of the agency are not licensed by the FCC. The FCC license for your agency -only- covers the agency and radios that they put on the system. That means that you will need to have permission from the licensee (not the chief, not anyone else) to add a radio to their system. You can look up the FCC license on the FCC.gov page, find out who the license holder is and talk to them. Make sure you get it in writing just to cover yourself.
A couple of things I'd add...
The radio needs to be properly installed. That means pulling power directly off the vehicle battery. Do not tap into any existing wiring for radio power.
If you want the radio to turn on/off with the ignition, that will need to be wired up and programmed.
The most important part of your installation is the antenna. Do not buy a cheap antenna/mount off e-Bay, Amazon, etc. and expect things to work. Use quality parts from Larsen, Laird, Comtelco, etc. Avoid the cheap Chinese knock off parts from Tram, Browning, any of the Amateur/hobby grade stuff. Have the antenna properly installed on a permanent mount on top of your vehicle. Have the antenna tested with an antenna analyzer or at least an SWR meter designed for the frequencies you use.
Also, when it comes to programming,
I'd really, strongly, suggest getting it programmed by who ever does the radios for your agency. There's a lot of places to make errors that can cause issues. You don't want to be "that guy" when it comes to this stuff. It's fairly easy to set radios up in such a way they can interfere with other agencies. By getting them programmed by someone who's experienced with that model radio and understands the license restrictions, you'll save a lot of headaches and potential risks to the agency FCC license. Not hard to do, but not for the beginner, either.
Those old Astro Spectras can have a number of issues. I'd suggest having a knowledgeable technician that knows how to work on that model radio put in on a service monitor to make sure it's working to factory specs.
Most of all, get help if you need it. This isn't like installing a CB, so avoid stereo shop installs, and the like. It really is worth having the equipment installed, tuned and tested.
