Karst springs are a natural result of karst water discharging to the surface through unimpeded pathways where the water table meets the surface. This study investigates the impact of alluvial deposits of varying thicknesses and permeabilities burying the main outlet (karst spring) of a well‐developed conduit network on karst drainage, including the development of hydraulic heads, drainage patterns and conduit‐matrix interactions in response to a positive base‐level shift. Numerical testing using FEFLOW on a simplified conceptual model of a hypothetical karst aquifer with six different model configurations was used to examine various drainage structures (with and without flow through a conduit), spring conditions (free vs. partially/fully clogged), sediment cover thickness (20 and 50 m), and hydraulic conductivity of the sediments (low and high). The numerical testing model incorporated one‐dimensional discrete feature elements to simulate conduit flow and coupled conduit‐matrix interactions. Results indicate that even with a fully plugged outlet, the conduit network remains a significant contributor to the drainage system, collecting water from the matrix in the recharge zone. As the outlet becomes buried, the hydraulic head increases along the conduit, forcing water back up into the matrix. The elevated hydraulic head in the karst system will cause new conduits to form at the contact between limestone and sediments, creating new potential spring sites (or reactivating existing paleo‐phreatic levels). Artesian conditions will occur below the low permeability sediments. These findings provide valuable insights into the responses of natural karst systems.