My MacBook Pro operating on OS X Yosemite 10.10.5 cannot detect my HP 8610 wireless printer once I replaced my router and modem with an Arris TG1672G modem/router combination issued by Time Warner. Both of our iPads continue to recognize the printer.

When you replace your Router and/or modem, the new one often uses a different range of "strictly private" IP Addresses. For example the old one could have used addresses in the 192.168.xxx.yyy range, the new one could use addresses in the 10.10.xxx.yyy range.

This leaves your printer behind on the old network, unreachable from the new Network.

What is needed is to make certain the printer gets a new Address in the correct range. That almost always must be done by fat-fingering it into the printer's own control panel. If you changed your Wi-Fi password, you will need to supply that new password as well in the same manner, to allow the Printer to talk on the new Wi-Fi network.