Inducing a magnetic gap at the Dirac point of the topological surface state (TSS) in a 3D topological insulator (TI) is a route to dissipationless charge and spin currents. Ideally, magnetic order is present only at the surface and not in the bulk, e.g. through proximity of a ferromagnetic (FM) layer. However, such a proximity-induced Dirac mass gap has not been observed, likely due to insufficient overlap of TSS and the FM subsystem. Here, we take a different approach, namely FM extension, using a thin film of the 3D TI Bi$_2$Te$_3$, interfaced with a monolayer of the lattice-matched van der Waals ferromagnet MnBi$_2$Te$_4$. Robust 2D ferromagnetism with out-of-plane anisotropy and a critical temperature of $\text{T}_\text{c}≈$~15 K is demonstrated by X-ray magnetic dichroism and electrical transport measurements. Using angle-resolved photoelectron spectroscopy, we observe the opening of a sizable magnetic gap in the 2D FM phase, while the surface remains gapless in the paramagnetic phase above T$_c$. This sizable gap indicates a relocation of the TSS to the FM ordered Mn moments near the surface, which leads to a large mutual overlap.