This white paper gives a brief summary of the time domain science that has been performed with the JCMT in recent years and highlights the opportunities for continuing work in this field over the next decade. The main focus of this document is the JCMT Transient Survey, a large program initiated in 2015 to measure the frequency and amplitude of variability events associated with protostars in nearby star-forming regions. After summarising the major accomplishments so far, an outline is given for extensions to the current survey, featuring a discussion on what will be possible with the new 850 micron camera that is expected to be installed in late 2022. We also discuss possible applications of submillimetre monitoring to active galactic nuclei, X-ray binaries, asymptotic giant branch stars, and flare stars.