Elastic scattering measurement for the ⁹Be+⁸⁹Y system has been carried out at near-barrier energies with the aim of investigating the effect of breakup on the elastic channel. The energy dependence of the optical model potential for the system gives an indication of the breakup threshold anomaly (BTA) for the system. An overall repulsive real part of the dynamic polarization potential (DPP) generated due to continuum couplings using the α+⁵He cluster structure for ⁹Be is consistent with the BTA behavior observed for the system. In contrast, an attractive real part of the DPP, at all energies, is observed for similar calculations carried out using the ⁸Be + n cluster structure. Coupling of the 1n transfer channel in addition to continuum couplings does not have a significant effect on the elastic scattering angular distributions. The experimental 1n transfer cross sections show better agreement with the corresponding values obtained using the ⁸Be + n cluster structure calculations. Inclusive breakup-α cross sections are observed to form a large fraction of the reaction cross sections, especially at below-barrier energies, suggesting the dominance of the breakup channel at these energies. This also supports the BTA behavior observed for the system, reflected as the presence of a reaction channel and thus the persistence of the imaginary potential at below-barrier energies.