To start with we define the Farey set $F_{\infty}$ as the set of all ideal vertices which produce punctures on a given Riemann surface and lie on the boundary of the Poincare disk. A pair $(\rho,\beta)$ is called a framed representation where $\rho\colon\pi_1(S_{g,n})\to\text{PSL}_2(\mathbb{C})$ is a representation and $\beta\colon F_{\infty}\to \mathbb{C}P^1$ is $\rho$-equivariant, called framing. Given a type-preserving non-degenerate framed representation framed representation $\rho\colon\pi_1(X) \to \text{PSL}_2(\mathbb{C})$ with no apparent singularities, we construct a $\rho$ equivariant harmonic map asymptotic to the framing.