Textile reinforced mortar (TRM) composites are an innovative solution for strengthening masonry structural elements due to their effectiveness and sustainability, as well as their compatibility with masonry substrates. As TRM composites are externally bonded to the surface of structural elements, the bond behaviour at the textile-mortar matrix and mortar matrix-substrate interfaces is a critical issue that needs to be investigated. In this study, an extensive study is carried out which includes a series of experimental tests combined with advanced numerical modelling with the aim to provide a better understanding of the bond behaviour of steel-TRM composites for strengthening a specific type of masonry which made by grey clay bricks. The experiments mainly consist of 28 single-lap shear bond tests on steel-TRM strengthened masonry elements. The effect of the masonry substrate condition, configuration of the textile, mechanical properties of the mortar matrix, and length of the bond are presented. The test results are discussed in terms of the full range of load-slip responses and failure modes. Then, an advanced numerical model based on simple interfacial local bond-slip constitutive laws is validated by agreement with the experimental findings. Finally, the numerical results are also used to evaluate the effective bond length and further understand the bond behaviour.