Brown dwarfs in the spectral range L9-T3.5, within the so called L/T transition, have been shown to be variable at higher amplitudes and with greater frequency than other field dwarfs. This strong variability allows for the probing of their atmospheric structure in 3D through multi-wavelength observations for studying the underlying physical mechanisms responsible for the variability. The few known strongly variable dwarfs in this range have been extensively studied. Now, more variables such as these need to be discovered and studied to better constrain atmospheric models. This is also critical to better understand giant exoplanets and to shed light on a number of possible correlations between brown dwarf characteristics and variability. Previous studies suggest an occurrence rate for strong variability (peak-to-peak amplitudes >2%) of up to 39% among brown dwarfs within the L/T transition. In this work, we aim to discover new strong variables in this spectral range by targeting ten previously unsurveyed brown dwarfs. We used the NOTCam at the Nordic Optical Telescope to observe 11 targets, with spectral types ranging from L9.5 to T3.5, in the J-band during October 2017 and September 2018. Using differential aperture photometry, we then analysed the light curves for significant variability using Lomb-Scargle periodogram algorithms and least squares fitting. We report first discoveries of strong and significant variability in four out of the ten targets (false alarm probability <0.1%), measuring peak-to-peak amplitudes up to 10.7+/-0.4% in J for the T1 dwarf 2MASS J22153705+2110554, for which we observe significant light curve evolution between the 2017 and 2018 epochs. We also report a marginally significant detection of strong variability, and confirm that the well known 2MASS J01365662+0933473 is still strongly variable three years after the last reported epoch. Finally, we present an extensive multi-epoch catalogue of strong variables reported in the literature and discuss possible correlations that are identifiable from the catalogue. We significantly add to the number of known strong variables, and through Poisson statistics infer an occurrence rate for strong variability among L9-T3.5 brown dwarfs of 40^+32^_19_%, which is in agreement with previous estimates. The new variables identified in this work are also excellently suited for extensive multi-wavelength observations dedicated to probing the 3D structure of brown dwarf atmospheres.