HSA is added to the solution of the compound in pH 7.4 buffer. We would like to quantify the bound and unbound compound concentration together by HPLC after. Therefore elimination of the binding to HSA is needed.
There are several approaches available to measuring binding of compounds to HSA, including equilibrium dialysis as suggested by Szabolcs. Some other ones include isothermal titration calorimetry, the Hummel-Dreyer method using size exclusion chromatography, and centrifugal ultrafiltration to separate free compound from HSA. Whatever method you choose, make sure the HSA you use is free of bound fatty acids.
Many compounds that bind to HSA have been shown to influence the tryptophan fluorescence. It may not be the case for your ligands but it is worth looking at since then you do not need to separate bound from free to get a binding constant.