Shell-model calculations are performed using NuShellX code in the model space $\pi( f_{5/2}, p_{3/2}, p_{1/2}, g_{9/2}) \otimes \nu(g_{9/2}, g_{7/2}, d_{5/2}, h_{11/2})$, which probe the proton core excitation from the interior of $Z = 38$ semiclosed shell and neutron core excitation from the interior of $N = 56$ semiclosed shell for the level structure of $^{89}Sr$. Our calculations show that the excitation of a single $d_{5/2}$ neutron across $N = 56$ semiclosed shell into the $h_{11/2}$ orbit should have great effects on the excited states of $^{89}Sr$. In addition, the systematic features of proton core excitation across $Z = 38$ semiclosed shell into the $g_{9/2}$ orbit and neutron core excitation across $N = 56$ semiclosed shell into the $g_{7/2}, s_{1/2}, d_{3/2}, h_{11/2}$ orbits in $N = 51$ isotones are discussed.