"That on the application of the owners, Messrs Thomas Dixon and Sons a new street on their property, situate off Cambrai Street and Olive Street be named Yew Street". (17th December 1890).
Along with Olive Street this street appeard for the first time in 1892. It is likely its name has a connection with the nearby St Matthew's Church which was completed in 1872. The yew tree has been associated with life, death & rebirth, signicant to both Druids and ancient Celtic people. Yew trees were also important for Christianity and were often planted church graveyards.
https://discovernorthernireland.com/whats-on/st-matthews-shankill-parish-church-ehod-2023-p759321