The Beryl Burton Cycleway is part of NCN636, the very narrow and steep climb west from Knaresborough which is heavily used by walkers, so that part is best skipped in IMO in the current crisis, due to limited social distancing possible. The alternate is use the A59 - westbound it, after a short distance, has its own cycletrack which initially climbs steeper than the road
and when it rejoins the main carriageway an immediate right turn takes you along a lane that meets NCN636 at the end of the Beryl Burton section. Alternatively the uphill the A59 is two lane so cyclists often stay on the main carriageway.
If heading east from Clint on NCN67 note there is a gate that has to opened to access the bridleway beyond which the bridleway goes up sharply; best to change to an appropriate gear before stopping at the gate.