In this article, utilizing the newly introduced concept of double controlled metric like space, we study the implicit relation along with $(\mathcal{F}, \mathcal{H})$-contractions through orbital admissible mappings. Our results extend, generalize and unify many well known results. Examples are also presented to justify the effectiveness of our new findings. Lastly, one application is presented in a system of non-linear integral equations to discuss the existence of a solution.