The upcoming beyond 5G (B5G) wireless networks target various innovative technologies, services, and interfaces such as edge computing (EC), ultra-reliable and low-latency communication (URLLC), backscatter communications, and TeraHertz (THz) technology-enabled inter-chip communications, and high capacity links. Although there are ongoing advances in the system/network level, it is crucial to introduce innovations at the device-level to efficiently support these novel technologies by addressing various practical constraints such as power limitations, computational capacity, and storage capacity. Considering the contemporary latency requirements of future consumer electronics (CE) (e.g., entertainment, gaming, etc), to enhance the commercial potential of “edge processing as service”, it is envisioned that URLLC will further evolve as enhanced-URLLC (e-URLLC). In this regard, this paper proposes a novel EC-enabled e-URLLC framework for the next-generation CE devices, named EC for CE (ECCE), in order to enable the support of e-URLLC in the wireless 6G era. Starting with the discussion on recent trends and advances in CE, the proposed framework and its importance in the 6G era are described. Subsequently, several potential enabling technologies and tools for the implementation of the proposed ECCE framework are identified along with a discussion on some interesting open research topics.