A philosophy among some Klingon houses that anyone that is willing to meet the Klingon idea of Honor and live up to it is a Klingon, their race and genes aside. "Klingon" is not a bloodline, but an idea. One that other peoples can adopt and strengthen.
New Klingon is a reaction to the fact that in the Klingon Empire genetic Klingons are increasingly out numbered by clients. More and more Klingon Houses are being forced into the warrior caste to maintain the Empire. Human Friends have pointed out the fate of Sparta on Earth that put all the non fighting skill into the hands of slaves. When foes armed the slaves, they were crushed from within.
The Klingon Empire is headed down that road the writing is on the wall.
New Klingons seek to co-opt the clients by spreading the idea of Klingon. There is no Klingon and other in the Empire, only Klingon.
This is violently opposed by Real Klingons