The Galactic Centre is known to have undergone a recent star formation episode a few Myr ago, which likely produced many T Tauri stars hosting circumstellar discs. It has been suggested that these discs may be the compact and dusty ionized sources identified as ‘G-clouds’. Given the Galactic Centre’s hostile environment, we study the possible evolutionary pathways these discs experience. We compute new external photoevaporation models applicable to discs in the Galactic Centre that account for the subsonic launching of the wind and absorption of UV photons by dust. Using evolutionary disc calculations, we find that photoevaporation’s rapid truncation of the disc causes them to accrete onto the central star rapidly. Ultimately, an accreting circumstellar disc has a lifetime ≲ 1 Myr, which would fail to live long enough to explain the G-clouds. However, we identify a new evolutionary pathway for circumstellar discs in the Galactic Centre. Removal of disc material by photoevaporation prevents the young star from spinning down due to magnetic braking, ultimately causing the rapidly spinning young star to torque the disc into a ‘decretion disc’ state which prevents accretion. At the same time, any planetary companion in the disc will trap dust outside its orbit, shutting down photoevaporation. The disc can survive for up to ∼10 Myr in this state. Encounters with other stars are likely to remove the planet on Myr time-scales, causing photoevaporation to restart, giving rise to a G-cloud signature. A giant planet fraction of ∼10 per cent
can explain the number of observed G-clouds.