Numerous tidal disruption event (TDE) candidates originating from galactic centres have been detected (e.g., by ${\it Swift}$ and ASASSN). Some of their host galaxies show typical characteristics of a weak active galactic nucleus (AGN), indicative of a pre-existing accretion disc around the supermassive blackhole (SMBH). In this work, we develop an analytic model to study how a pre-existing accretion disc affects a TDE. We assume the density of the disc $ρ∝ R^{-λ}$, $R$ being the radial distance from the SMBH and $λ$ varying between $0.5-1.5$. Interactions between the pre-existing accretion disc and the stream of the tidally disrupted star can stall the stream far from the SMBH, causing a sudden drop in the rate of fallback of gas into the SMBH. These interactions could explain the steep cut-off observed in the light curve of some TDE candidates (e.g., ${\it Swift}$ J1644 and J2058). With our model, it is possible to use the time of this cut-off to constrain some properties pertaining to the pre-existing accretion disc, such as $λ$ and the disc viscosity parameter $α$. We demonstrate this by applying our theory to the TDE candidates ${\it Swift}$ J1644, J2058 and ASASSN-14li. Our analysis favours a disc profile with $λ∼1$ for viscosity parameters $α∼0.01-0.1$. ; Comment: 9 pages, 7 figures