The past decade represented the kick-off and settlement of multi-messenger and time-domain astronomy, coincident with the blooming of transient TeV astronomy. Over the past decade, new sources of very-high-energy (VHE) gamma rays have been discovered, opening new physics in this energy regime: the discovery of a TeV counterpart of long gamma-ray bursts (GRBs) via the detection of afterglow emission, the association of a neutrino with a flaring blazar or the VHE signal of hadronic origin from a nova. Many of these new VHE transient sources have been discovered with Cherenkov telescopes located at the Roque de los Muchachos (ORM) in the Canary Island of La Palma, one of the only three observatories hosting this type of instrumentation in the world. In this contribution, we review the TeV sources of transient nature that have been identified in the VHE regime in a multi-messenger context, making use of the MAGIC telescopes and the first Larged-Size Telescope (LST-1), and we briefly outlook for new perspectives with the future Cherenkov Telescope Array Observatory (CTAO), whose northern array will be located at ORM.