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We present a new volume-limited sample of L0-T8 dwarfs out to 25 pc defined entirely by parallaxes, using our recent measurements from UKIRT/WFCAM along with Gaia DR2 and literature parallaxes. With 369 members, our sample is the largest parallax-defined volume-limited sample of L and T dwarfs to date, yielding the most precise space densities for such objects. We find the local L0-T8 dwarf population includes $5.5\%\pm1.3\%$ young objects ($\lesssim$200 Myr) and $2.6\%\pm1.6\%$ subdwarfs, as expected from recent studies favoring representative ages $\lesssim$4 Gyr for the ultracool field population. This is also the first volume-limited sample to comprehensively map the transition from L to T dwarfs (spectral types $\approx$L8-T4). After removing binaries, we identify a previously unrecognized, statistically significant (>4.4$σ$) gap $\approx$0.5 mag wide in $(J-K)_{\rm MKO}$ colors in the L/T transition, i.e., a lack of such objects in our volume-limited sample, implying a rapid phase of atmospheric evolution. In contrast, the most successful models of the L/T transition to date $-$ the "hybrid" models of Saumon & Marley (2008) $-$ predict a pile-up of objects at the same colors where we find a deficit, demonstrating the challenge of modeling the atmospheres of cooling brown dwarfs. Our sample illustrates the insights to come from even larger parallax-selected samples from the upcoming Legacy Survey of Space and Time (LSST) by the Vera Rubin Obsevatory.