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We present the detection of 107 pulsars with interstellar scintillation arcs at 856--1712\,MHz, observed with the MeerKAT Thousand Pulsar Array Programme. Scintillation arcs appear to be ubiquitous in clean, high S/N observations, their detection mainly limited by short observing durations and coarse frequency channel resolution. This led the survey to be sensitive to nearby, lightly scattered pulsars with high effective velocity -- from a large proper motion, a screen nearby the pulsar, or a screen near the Earth. We measure the arc curvatures in all of our sources, which can be used to give an estimate of screen distances in pulsars with known proper motion, or an estimate of the proper motion. The short scintillation timescale in J1731$-$4744 implies a scattering screen within 12\,pc of the source, strongly suggesting the association between this pulsar and the supernova remnant RCW 114. We measure multiple parabolic arcs of 5 pulsars, all of which are weakly scintillating with high proper motion. Additionally, several sources show hints of inverted arclets suggesting scattering from anisotropic screens. Building on this work, further targeted MeerKAT observations of many of these pulsars will improve understanding of our local scattering environment and the origins of scintillation; annual scintillation curves would lead to robust screen distance measurements, and the evolution of arclets in time and frequency can constrain models of scintillation.