As devices scale closer to the atomic size, a complete understanding of the physical mechanisms involving defects in high-κ dielectrics is essential to improve the performance of electron devices and to mitigate key reliability phenomena, such as Random Telegraph Noise (RTN). In fact, crucial aspects of defects in HfO2 are still under investigation (e.g., the presence of metastable states and their properties), but it is well known that oxygen vacancies (V+s) and oxygen ions (O0s) are the most abundant defects in HfO2. In this work, we use simulations to gain insights into the RTN that emerges when a constant voltage is applied across a TiN/(4 nm)HfO2/TiN stack. Signals exhibit different RTN properties over bias and, thus, appear to originate from different traps. Yet, we demonstrate that they can be instead promoted by the same O0s which change their capture (τc) and emission (τe) time constants with the applied bias, which, in turn, changes the extent of their electrostatic interactions with the traps that assist charge transport (V+s). For a certain bias, RTN is given by the modulation of the trap-assisted current at V+s induced by trapping/detrapping events at O0s, which are, in turn, influenced by the bias itself and by trapped charge at nearby O0s. In this work, we demonstrate that accounting for the effect of trapped charge is essential to provide accurate estimation of the RTN parameters, which allow us to retrieve information about traps and to explain key mechanisms behind complex RTN signals.