A competitive binding assay requires some means of distinguishing between the bound and free states of the "probe". In your example, the probe could be either the peptide or the receptor. I don't know of a simple method using absorbance to distinguish between free and bound probe, in this case. You would probably have to set up an ELISA, in which one component is attached to the surface of the plate and an antibody is used to detect the other component after a wash step to remove the unbound form.

A simple method, in my view, to do a competitive binding assay uses fluorescence polarization. This requires a specialized plate reader with fluorescence polarization capability. Such plate readers are likely to be available at a high-throughput screening facility, and fluorescence polarization-based competitive binding assays are very common. In this case, a fluorescent dye would be attached covalently to the peptide at a position that would not cause it to interfere with binding to the receptor. When the peptide is bound to the receptor, the fluorescence polarization is higher than when the peptide if free. No washing is required.

Here is 2 examples.

Article A High-Throughput-Compatible Fluorescence Anisotropy-Based A...

https://pubmed.ncbi.nlm.nih.gov/24820111/

Thank you so much Adam B Shapiro for the insights. Without asking, I would have probably proceeded with the UV absorbance method. I had ELISA in mind as well but I wanted to do a hit and trial attempt for the UV method, but I think I should consider fluorescence polarization as well. Thank you, again!