In this paper, we presented the 23.3 yr of pulsar timing results of PSR J1456−6413 based on the observations of Parkes 64 m radio telescope. We detected two new glitches at MJD 57093(3) and 59060(12) and confirmed its first glitch at MJD 54554(10). The relative sizes (Δν/ν) of these two new glitches are 0.9 × 10−9 and 1.16 × 10−9, respectively. Using the "Cholesky" timing analysis method, we have determined its position, proper motion, and two-dimensional transverse velocities from the data segments before and after the second glitch, respectively. Furthermore, we detected exponential recovery behavior after the first glitch, with a recovery timescale of approximately 200 days and a corresponding exponential recovery factor Q of approximately 0.15(2), while no exponential recovery was detected for the other two glitches. More interestingly, we found that the leading component of the integral pulse profile after the second glitch became stronger, while the main component became weaker. Our results will expand the sample of pulsars with magnetosphere fluctuation triggered by the glitch event.