Radio pulsars are rapidly rotating neutron stars that emit radio emission from their magnetic poles. As the poles sweep across our radio telescope we detect "pulses" of emission much like the ticks of a clock. On long timescales the stability of these "clocks" rivals the precision of the atomic clocks on Earth and furnishes us with tools with which to study the extremes of energy, density, temperature, and gravitational and magnetic fields. With MeerTRAP it will be possible to discover many new pulsars, but in particular to expand the range of sources known by using the unique MeerTRAP observing approach to discover the more "variable" systems as discussed below.

Relativistic binaries containing pulsars can be used for tests of fundamental physics; the more extreme the binary the better. A pulsar in a compact and eccentric orbit with another compact object like a white dwarf, another neutron star, or a black hole is highly sought after. These objects allow us to perform important tests of gravity theories: the strong equivalence principle, gravitational radiation, and the "cosmic censorship conjecture" to name just a few.

Transition objects are neutron stars recently found to transition between radio emitting binary millisecond pulsar (MSP) and Low Mass X-ray Binary phases where radio pulsations cease. These systems provide vital clues to the mass outflow, accretion physics and emission processes involving neutron stars. They also tell us about the birth periods and masses of MSPs and thus have important consequences for the neutron star equation of state.

Discovering pulsars in binary systems is no easy task. Their rapid orbital motion causes their apparent pulse frequency to be Doppler shifted and therefore vary significantly over time scales shorter than a typical radio observation, making them difficult to detect by search algorithms. The deleterious effects of orbital motion can be computationally countered, but that multiplies the compute cost of a search by a factor that grows with at least the square of the integration time. At the end of the day, algorithmic cleverness is no substitute for a larger telescope. Not only will MeerKAT allow us to explore the Southern radio skies with unprecedented sensitivity, but the MeerTRAP approach of making many visits to the same piece of sky increases the chances of catching a binary pulsar in an ideal orbital configuration, where the effects of binary motion are lowest.

Rotating RAdio Transients (RRATs) are rotating neutron stars that emit extremely infrequently, less than a second per day. If they are distinct from pulsars then there may be too many neutron stars in the Galaxy compared to what is expected from the supernova rate. A much larger sample, with measured ages, magnetic field strengths and accurate positions, is required. The discovery of a large sample of RRATs will benefit greatly from the wide field of view and regular visits to the same regions possible with MeerTRAP. Accurate measurement of their position will be possible, aiding the determination of the spin parameters.

Intermittent pulsars are a pulsar class that emit for up to hundreds of days and then turn off completely for up to hundreds of days. These switches are accompanied by changes in the rate at which the pulsar spins down; indicating significant changes in the pulsar magnetosphere. At present only a few systems are known, as the long periods of radio silence mean they are very difficult to detect. More sources will provide understanding of the neutron star population size, the radio emission-spin properties connection, and relation to other radio variability like nulling and moding. The minute to month cadences of MeerTRAP give an unbiased range of timescales to detect these sources.