There are two sites marked 'Hag Head' on the map linked in reply #1. (On a later map the northerly Hag Head is marked as Hag Head Laithe).
On the 1847 tithe map the northerly site is in the township of Draughton (parish of Skipton). It is labelled on the tithe map as Hagghead, owner the Duke of Devonshire, occupier "Shiers" (very unusual on a tithe record to have an incomplete name). Whoever Shiers is, he has a large holding of ~300 acres in the vicinity. Looking at a few plots along the parish boundary it seems that the Duke of Devonshire's holdings did not extend south across the parish boundary into Addingham.
On the 1843 tithe map the southerly Hag Head lies just within the township of Addingham (in the parish of Addingham). Although the farmhouse is clearly shown on the map with a plot number of 16, it is not listed separately in the records. However the neighbouring land is all owned by Henry Alcock Bramley and occupied by Timothy Brear.
In the 1841 census a Timothy Breare is a farmer at Haghead in Addingham, and is still there in 1851. This must be the southerly farm.
I went looking for 'Shiers' in the 1841 census, and when I checked a Leonard Shiers, farmer, (abode unclear, but not Hag Head), I noticed that his neighbour immediately preceding him is Martin West, abode Hag Head, farmer age 76, plus 11 other family members (all West).
Thus it seems that the northerly Hag Head was the West's farm. Perhaps it had passed on to the Shiers family between 1841 and 1847?