Lurie develops in Section 3.1.2 of Higher Algebra a notion of operadic left Kan extension used to compute free algebras, giving a left adjoint $\mathrm{Alg}_{\mathcal{O}}(\mathcal{C})\to\mathrm{Alg}_{\mathcal{O}'}(\mathcal{C})$ to the forgetful functor $\mathrm{Alg}_{\mathcal{O}}(\mathcal{C})\to\mathrm{Alg}_{\mathcal{O}'}(\mathcal{C})$ associated to any map of $\infty$-operads $\mathcal{O}\to\mathcal{O}'$.

There's a number of constructions in the $1$-categorical setting that resemble this notion a bit, including monoidal Kan extensions (see also here, here, here, here, and here) and multicategorical Kan extensions. However, (as far as I understand) these don't quite capture the general notion developed by Lurie.

Is there a detailed treatment specifically for $1$-categorical operadic left Kan extensions somewhere in the categorical literature?