We investigate the effect of non-Hermitian Gamma interaction on the phase transitions and magnetic correlations for the transverse field Ising chain. We demonstrate that apart from the gapped antiferromagnetic and paramagnetic phases, there is a gapless phase induced by parity-time symmetry breaking, where the system exhibits long-range and short-range spin-nematic correlations in different regions divided by the quantum critical line determined from the correlation function and the subsystem entanglement entropy. Furthermore, we reveal that the parity-time symmetry breaking leads to the emergence of dynamical spin-nematic correlation, which also suggests a way of characterizing the spin-nematic map through non-equilibrium dynamics. Our findings show rich quantum phases stem from the competition among the Ising interaction, transverse field and non-Hermitian Gamma interaction, as well as providing a scheme for generating spin-nematic correlation in the spin chain.