I can only repeat what I said before: these ways *are* the A516.  They do not have their OSM trunk status because of the connections to the A38, but because the green-signed A516 runs here on its way to the the A50 junction at Hilton.  It is just a free-flow merge of 2 nearly equal status A roads.  The only part of the A516 that does not carry its own ref is where the carriageway is shared with the main run of the A38 (and following the A516 route actually has its own continuous nearside lane both ways for the short distance until it divides again).  By this logic, how much of the continuation of the A516 would be _link? - to the Mickleover S turns/roundabout?