Glaciers worldwide are becoming increasingly debris-covered, yet many parts within the coupled glacier-debris system are not well-understood. While the insulating effect of debris is well-known, observations of debris cover are scarce, often limited by logistical challenges. The main aim of the study is to better understand the complex transient glacier response and debris-induced feedbacks through numerical flow modelling. We present a newly developed 1-dimensional flowline model that couples ice flow, depth-resolved debris transport, and debris cover impact on mass balance. This approach allows for a detailed examination of the dynamics of debris-covered glaciers under transient forcing conditions of climate and debris input over extended timescales. Our results indicate that low-amplitude, decade-scale variability in debris or climate forcing does not significantly impact glacier evolution. However, large debris supply events can have a sustained impact. We find that debris-covered glacier response to warming climate forcing is non-monotonic, with distinct phases of thinning, retreat, and long-term re-advance. We attribute this to a separate, longer timescale process of englacial debris transportation. Additionally, feedbacks in the englacial debris trajectory and complex bed topography further increase the non-linearity of transient glacier response.