Hi,
It would help if you could post information about the exact printer make and model.
With an AirPrint-compatible model, you should not have to use additional apps. An AirPrint printer must be connected to the same network (Wi-Fi router) as the iPad (and the Mac).
Use AirPrint to print from your iPhone or iPad - Apple Support
Generally speaking, if there is a problem with AirPrint printing, it may be a good idea to try a full power-cycle sequence (including the router): Power off the router, the printer, the iPad, the Mac, and all other devices/computers. Wait two to three minutes. Power on the router. Wait two to three minutes. Power on the printer. Wait a minute or two. Power on the iPad and the Mac. Finally, power on all other devices/computers.
If a network printer is not an AirPrint model, it may still be possible to print from an iPad via the Wi-Fi router if the printer manufacturer provides a special iPadOS app.
If the printer is a USB-only model, and a Mac has drivers for it, a Mac app like Printopia can be used for printing from an iPad. In this case, the Mac connected to the network would act as a print server.