This is the Route 1&9T Extension (New Road) under the Lincoln Tunnel Access Project. From what I could find, there are three contracts to this roadway - this segment is Contract 1, which is complete. Found this document that shows its progress: https://www.nj.gov/transportation/capital/stip2433/sec11/pdf/njtpa.pdf
Eventually the full extension of the roadway will fly over the Croxton Intermodal Terminal going SW, go under the NJ Transit lines, and join with Westside Avenue. One of the slides in this presentation shows the future alignment: https://0c337598-168f-4f94-ad4c-29cfee3567ca.filesusr.com/ugd/98f1dc_ff7e7c2802564755abf19e5121865cb9.pdf
Not sure if NJTPA would open this segment when it's part of a larger roadway? If anyone local here can take a look to confirm, it'd be appreciated.