This segment of Brierley Drive (between Castle Eden Walkway and a point hundreds of metres further east) exists only as a faint contour in a thicket. 
There is no navigable path.
The route does pick up again, but I have not mapped that point yet. 

Some nearby images for context. 
https://postimg.cc/gallery/T6xw7vP4

Traces of the drive contour are evident at the woodland edge, but parts have been obliterated by recent landscaping. 
https://postimg.cc/v4XZCGcL
https://postimg.cc/RN7FQ7mY