We study the effects of phase transition in the equation of state of a neutron star containing a condensate of anti-kaons, using an effective model with derivative couplings. In our formalism, nucleons interact through the exchange of σ, ω, ϱ, and δ meson fields in the presence of electrons and muons to accomplish electric charge neutrality and beta equilibrium. The phase transition to the anti-kaons condensate was implemented through the Gibbs conditions combined with the mean-field approximation, giving rise to a mixed phase of coexistence between hadron matter and the condensed of anti-kaons. In conclusion, we have found that isovector meson degrees of freedom contribute to tighten the Equation of State of Neutron Stars.