In this paper, we show that the interfaces in the FK Ising model at criticality in a domain with 4 marked boundary points and wired–free–wired–free boundary conditions conditioned on a specific internal arc configuration of interfaces converge in the scaling limit to the hypergeometric SLE (hSLE). The arc configuration consists of a pair of interfaces and the scaling limit of their joint law can be described by an algorithm to sample the pair from an hSLE curve and a chordal SLE (in a random domain defined by the hSLE).