Having looked at the second instance of the name in the clip kindly posted by bbart, I see no reason to alter my initial reading.
[I was hoping that the name might be An[ne] Turlington, because John Turlington of Birstall, Leicestershire married Ann Leverett there in 1722.
I see no problem with this
an Torlinton in the will being the same as
Anne Turlington elsewhere. The variation in spelling is well within what we would expect in writings of this period.
Indeed this is exactly what I referred to in the second sentence of my first post.