Springer⁵, has been studied and defined Union curves of a Riemannian hypersurface Mishra¹, has investigated the properties of these curves in a subspace of a Riemannian space. Further, Saxena and Behari², studied Hypersurfaces of Kaehler manifold. Singh³, studied and defined hypernormal curves of a Finsler subspace. In the present paper, we have studied on special, Union and hyper-asymptotic curves of a Tachibana Recurrent Hypersurface also several theorems have established and proved therein.