That depends on the device software.
Generally when turned to AP mode the device should only work as a DHCP client and not a server. In any case you should always manually assign IP addresses to static devices on your network, simply to be able to access them later.
Check the DHCP pool your router is configured to use. Enter the AP config and set a static IP outside the pool (so you don't have any address conflicts). Turn off the DHCP server if that doesn't happen automatically and save settings. After saving you will need to type the new (static) address on your browser to re-access the AP. I would also suggest turning off firewall (on AP) if the router has it's firewall enbled, two firewalls on the network may cause problems.
An AP shouldn't be a DHCP server that's why the option is disabled.
There must be only one DHCP server on the network also, very important!!!
For your network devices to be able to work together you must have them all on the same vlan. Meaning they all need to have the SAME first three components in their IP address (192.168.0.xxx) if that is the range your DHCP server is issuing also. Using different vlans will not work.
Try setting the DHCP pool from 192.168.0.20 - 192.168.0.50, allow the first 20 addresses for manual issue to any network devices and static clients in your network like STBs, game consoles, smart TVs, media players etc. All of these devices will always be connected and some may need port forwarding so it is best to issue their addresses manually. Use the DHCP server to issue addresses to mobile devices (laptops, phones, tablets etc) that aren't always going to be connected. Doing this will take some of the work load off your router and you will also know the address of the devices connected.
Think of what would happen if one of your APs was down or you wanted to make a change in the configuration. With DHCP, how would you know its address? You would need to connect to the router and check the connected devices to find the one you are looking for. That doesn't sound too hard right, what would happen if the AP doesn't have a host name, how would you know which is which?