  High-quality light curves from space missions have opened up a new window on
the rotational and pulsational properties of magnetic chemically peculiar (mCP)
stars and have fuelled asteroseismic studies. They allow the internal effects
of surface magnetic fields to be probed and numerous astrophysical parameters
to be derived with great precision. We present an investigation of the
photometric variability of a sample of 1002 mCP stars discovered in the LAMOST
archival spectra with the aims of measuring their rotational periods and
identifying interesting objects for follow-up studies. TESS photometry was
available for 782 mCP stars and was analysed using a Fourier two-term frequency
fit to determine the stars' rotational periods. The rotational signal was then
subtracted from the light curve to identify non-rotational variability. A
pixel-level blending analysis was performed to check whether the variability
originates in the target star or a nearby blended neighbour. We investigated
correlations between the rotational periods, fractional age on the main
sequence, mass, and several other observables. We present rotational periods
and period estimates for 720 mCP stars. In addition, we identified four
eclipsing binary systems that likely host an mCP star, as well as 25 stars with
additional signals consistent with pulsation (12 stars with frequencies above
10 d$^{-1}$ and 13 stars with frequencies below 10 $^{-1}$). We find that more
evolved stars have longer rotation periods, in agreement with the assumption of
the conservation of angular momentum during main-sequence evolution. With our
work, we increase the sample size of mCP stars with known rotation periods and
identify prime candidates for detailed follow-up studies. This enables two
paths towards future investigations: population studies of even larger samples
of mCP stars and the detailed characterisation of high-value targets.
