  We report on the subpulse modulation properties of 1198 pulsars using the
Thousand-Pulsar-Array programme on MeerKAT. About 35% of the analysed pulsars
exhibit drifting subpulses which are more pronounced towards the deathline,
consistent with previous studies. We estimate that this common phenomenon is
detectable in 60% of the overall pulsar population if high quality data were
available for all. This large study reveals the evolution of drifting subpulses
across the pulsar population in unprecedented detail. In particular, we find
that the modulation period $P_3$ follows a V-shaped evolution with respect to
the characteristic age $\tau_c$, such that the smallest $P_3$ values,
corresponding to the Nyquist period $P_3>\sim2$, are found at
$\tau_c>\sim10^{7.5}$ yr. The V-shaped evolution can be interpreted and
reproduced if young pulsars possess aliased fast intrinsic $P_3$, which
monotonically increase, ultimately achieving a slow unaliased $P_3$.
Enhancement of irregularities in intrinsic subpulse modulation by aliasing in
small $\tau_c$ pulsars would explain their observed less well defined $P_3$'s
and weaker spectral features. Modelling these results as rotating subbeams,
their circulation must slow down as the pulsar evolves. This is the opposite to
that expected if circulation is driven by ExB drift. This can be resolved if
the observed $P_3$ periodicity is due to a beat between an ExB system and the
pulsar period. As a by-product, we identify the correct periods and spin-down
rates for 12 pulsars, for which harmonically related values were reported in
the literature.
