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ABSTRACT A wide variety of Galactic sources show transient emission at soft and hard X-ray energies: low- and high-mass X-ray binaries containing compact objects, isolated neutron stars exhibiting extreme variability as magnetars as well as pulsar-wind nebulae. Although most of them can show emission up to MeV and/or GeV energies, many have not yet been detected in the TeV domain by Imaging Atmospheric Cherenkov Telescopes. In this paper, we explore the feasibility of detecting new Galactic transients with the Cherenkov Telescope Array Observatory (CTAO) and the prospects for studying them with Target of Opportunity observations. We show that CTAO will likely detect new sources in the TeV regime, such as the massive microquasars in the Cygnus region, low-mass X-ray binaries with low-viewing angle, flaring emission from the Crab pulsar-wind nebula or other novae explosions, among others. Since some of these sources could also exhibit emission at larger time-scales, we additionally test their detectability at longer exposures. We finally discuss the multiwavelength synergies with other instruments and large astronomical facilities.