During T cell activation, biomolecular condensates form at the immunological synapse (IS) through multivalency-driven phase separation of LAT, Grb2, Sos1, SLP-76, Nck, and WASP. These condensates move radially at the IS, traversing successive radially-oriented and concentric actin networks. To understand this movement, we biochemically reconstituted LAT condensates with actomyosin filaments. We found that basic regions of Nck and N-WASP/WASP promote association and co-movement of LAT condensates with actin, indicating conversion of weak individual affinities to high collective affinity upon phase separation. Condensates lacking these components were propelled differently, without strong actin adhesion. In cells, LAT condensates lost Nck as radial actin transitioned to the concentric network, and engineered condensates constitutively binding actin moved aberrantly. Our data show that Nck and WASP form a clutch between LAT condensates and actin in vitro and suggest that compositional changes may enable condensate movement by distinct actin networks in different regions of the IS.