In the fast-developing field of tissue engineering there is a constant demand for new materials as scaffolds for cell seeding, which can better mimic a natural extracellular matrix as well as control cell behavior. Among other materials, polysaccharides are widely used for this purpose. One of the main candidates for scaffold fabrication is alginate. However, it lacks sites for cell adhesion. That is why one of the steps toward the development of suitable scaffolds for cells is the introduction of the biofunctionality to the alginate structure. In this work we focused on bone-sialoprotein derived peptide (TYRAY) conjugation to the molecule of alginate. Here the comparison study on four different approaches of peptide conjugation was performed including traditional and novel modification methods, based on 1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide/N-hydroxy succinimide (EDC/NHS), 4-(4,6-dimethoxy-1,3,5-triazine-2-yl)-4-methylmorpholinium chloride (DMTMM), thiol-Michael addition and Cu-catalyzed azide–alkyne cycloaddition reactions. It was shown that the combination of the alginate amidation with the use of and subsequent Cu-catalyzed azide–alkyne cycloaddition led to efficient peptide conjugation, which was proven with both NMR and XPS methods. Moreover, the cell culture experiment proved the positive effect of peptide presence on the adhesion of human embryonic stem cells.