This paper presents an Orthogonal Time Frequency Space (OTFS) waveform application along with a high altitude platform station (HAPS) relaying for remedying severe Doppler effects in non-terrestrial networks (NTNs). Taking practical challenges into consideration, HAPS is exploited as a decode and forward relay node to mitigate the high path loss between a satellite and a base station (BS). In addition, a maximum ratio transmission scheme with multiple antennas at the LEO-satellite is utilized to maximize Signal-to-Noise Ratio (SNR). A shadowed Rician fading model is employed for the channel realization between the LEO-satellite and the HAPS while Nakagami-m is used between the HAPS and the BS. We derive the closed-form expression of the outage probability (OP) for the end-to-end system. The theoretical and simulation results demonstrate that the OP can significantly decrease when the OTFS order and the number of transmit antennas increase.