Designing a “task” level between a client and a network that organizes synchronous network / api calls

For the application I'm working on, we have many api calls that do certain things. Usually each thing requires more than one api call. What I want to create is the middle level, where the user interface / client can simply say that it is performing a specific task, the middle level will call this task, and the task will process the entire sequence of api calls.

I find it difficult to choose the right design templates. Basically, I was thinking of a mediation type template that mediates the interaction between the user interface, network, and tasks. And everything will speak only with the mediator, but then this can make the mediator too complicated. Another requirement is that tasks can consist of other tasks (one task may depend on another task and cause it to wait for its completion).

Is there a common design pattern associated with what already exists?