Distributed Execution Frameworks (DEFs) such as Apache Spark have become ubiquitous as a solution for the execution of user-defined jobs to process terabytes of data across hundreds of nodes. One of the key costs of DEFs is scheduling of which parts of each job are placed on each host; better scheduling decisions provide lower overall execution time for each job, more efficient resource usage, and reduced energy consumption. Existing DEFs use a static approach to scheduling, either with a single generalised scheduler which aims to be a good fit for most workloads, or with a special-purpose scheduler which is tuned to optimise for a particular kind of workload. In both cases the scheduling implementation is fixed at design-time such that the DEF is unable to adjust to the actual characteristics of workloads that arrive at deployment time. In this paper we introduce an emergent scheduler for Distributed Execution Frameworks. This scheduler can be composed and re-composed at runtime from a set of different building blocks, allowing the system to dynamically provide the benefits of differing scheduling policies over time depending on the actual properties of incoming workloads - with improved performance and resource usage. In this paper we present the overall design of our emergent scheduler, we discuss the theoretical design space of different scheduling approaches, and we examine a specific research question to determine the correlation between workload properties and scheduling performance for different scheduler implementations. Our results are based on a real implementation of our emergent DEF running across multiple hosts in a real datacentre, and our implementation is made available as open-source software.