Easy response? Yes it will. 

More detailed is that it causes a double nat. 

some systems play nicely with a double nat and others done. 

Simplest fix is to put the SBG7400 in bridge (modem only) mode and let the tplink handle router/wireless. 

There’s other options but that’d be the simpliest. 

More detailed would be to leave the SBG in router mode and set the tplink in access point mode. 

Just make sure they use different ssid’s and are on different wifi channels to prevent interference. 

That’d let you use the arris for closer devices (because it has more capable close range wifi) and the tplink for the devices on the peripheral.