To start with we define the Farey set $F_{\mathrm{\infty }}$ 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 $\rho :{\pi }_1(S_{g,n})\to {\text{PSL}}_2(\mathbb{C})$ is a representation and $\beta :F_{\mathrm{\infty }}\to \mathbb{C}{P}^1$ is $\rho$-equivariant, called framing. Given a type-preserving non-degenerate framed representation framed representation $\rho :{\pi }_1(X)\to {\text{PSL}}_2(\mathbb{C})$ with no apparent singularities, we construct a $\rho$ equivariant harmonic map asymptotic to the framing.