This website visualises the Public Rights Of Way (PROW) Geographic Information System (GIS) data provided by Buckinghamshire Council and highlights footpaths on OSM that either do not have designation tags or are unmapped. 

https://osm.mathmos.net/prow/progress/bucks/-/little-missenden/

Sometimes footpaths genuinely do not exist on the ground so it's necessary to survey them before adding them to OSM, unless you know the route off by heart.

If you can confirm it exists and feel comfortable adding designation tags, this is what the footpath should be (including when the footpath shares a private road/driveway):

designation=public_footpath
prow_ref=Little Missenden Footpath 19

You can also see green (for footpath) and red (for bridleway) highlighted when editing by enabling "public rights of way" in the backgrounds tab, but you'll need Rob's website for the PROW reference number.