Part of the challenge of paddling the New is getting an idea of whether its flow is in without driving there to find out. There is no gage on the New and the next gage downstream on the Trinity doesn't always correlate well to New River flows. The best bet is to look at the flows for the Salmon River system. The South Fork Salmon is just over the mountain from the New and, like the New, is entirely free-flowing with no dams or diversions.
Dreamflows gives a rough estimate for the South Fork Salmon. Look for a flow of 3000 cfs on the main stem Salmon River at the Somes Bar gauge for a medium flow on the New