DanSpen101
Walked in the area recently, didn't do this particular path so can't be 100% sure where it goes but I think it could be a path organised by National Trust that leads to the coast via the old airfield. At the Birling Gap cafe/ visitor centre, a hand sketched map made by the NT was available showing a footpath near this note. 

Link to the map I got from NT website: https://nt.global.ssl.fastly.net/documents/maps/1431729729010-birling-gap-and-the-seven-sisters.pdf

We saw variants of the same map on signage at various points along the coast path. Not my picture but just like this: https://www.geograph.org.uk/photo/5861522

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Also, this map that we saw posted in the seven sisters car park at Friston Forest shows a slightly alternate version of the path.
https://www.sevensisters.org.uk/plan-your-visit/explore-by-map/

I'm not local so can't check it out myself