Agents that can simultaneously activate latent HIV, increase immune activation and enhance the killing of latently-infected cells represent promising approaches for HIV cure. Here, we develop and evaluate a trispecific antibody (Ab), N6/αCD3-αCD28, that targets three independent proteins: (1) the HIV envelope via the broadly reactive CD4-binding site Ab, N6; (2) the T cell antigen CD3; and (3) the co-stimulatory molecule CD28. We find that the trispecific significantly increases antigen-specific T-cell activation and cytokine release in both CD4 ⁺ and CD8 ⁺ T cells. Co-culturing CD4 ⁺ with autologous CD8 ⁺ T cells from ART-suppressed HIV ⁺ donors with N6/αCD3-αCD28, results in activation of latently-infected cells and their elimination by activated CD8 ⁺ T cells. This trispecific antibody mediates CD4 ⁺ and CD8 ⁺ T-cell activation in non-human primates and is well tolerated in vivo. This HIV-directed antibody therefore merits further development as a potential intervention for the eradication of latent HIV infection.