In this work, we propose a theoretical and experimental investigation of the interaction of guided pure shear horizontal (SH) wave within a uniaxial multilayered TbCo2/FeCo thin film deposited on Quartz ST-90°X cut in a delay line configuration. We evaluate theoretically the evolution of phase velocity as a function of magnetic field and experimentally the variation of S21 transmission coefficient (amplitude and phase). An equivalent piezomagnetic model based on pure magnetoelastic coupling was used (developed allowing us) to calculate the elastic stiffness constants of the multilayer as a function of the bias magnetic field. The model was also implemented for acoustic waves dispersion curves calculation. We show that the evolution of the phase velocity with respect to the bias magnetic field is dominated by the C66 elastic stiffness constant as expected for the case of shear horizontal surface acoustic wave. In the fabricated device, both fundamental and third harmonic shear mode are excited at 410 MHz and 1.2 GHz, respectively. For both modes, the theoretical and experimental results are in agreement. At 1.2 GHz the guiding of the acoustic wave in the ferromagnetic thin film enhances the sensitivity to the bias magnetic field with a maximum phase velocity shift close to 2.5 % and an attenuation reaching 500 dB/cm, for a sensitivity as high as 250 ppm/Oe, which is better than what has been reported in literature so far. We also report that, from a specific ratio between the thin film thickness and the acoustic wavelength, the bias magnetic field can induce a breaking of the acoustic wave polarization, leading to an acoustic mode conversion.