High Dynamic Range (HDR) Wide Color Gamut (WCG) Ultra High Definition (4K/UHD) content has become increasingly popular recently. Due to the increased data rate, novel video compression methods have been developed to maintain the quality of the videos being delivered to consumers under bandwidth constraints. This has led to new challenges for the development of objective Video Quality Assessment (VQA) models, which are traditionally designed without sufficient calibration and validation based on subjective quality assessment of UHD-HDR-WCG videos. The large performance variations between different consumer HDR TVs, and between consumer HDR TVs and professional HDR reference displays used for content production, further complicates the task of acquiring reliable subjective data that faithfully reflects the impact of compression on UHD-HDR-WCG videos. In this work, we construct a first-of-its-kind video database composed of PQ-encoded UHD-HDR-WCG content, which is subsequently compressed by H.264 and HEVC encoders. We carry out a subjective study on a professional 4K-HDR reference display in a controlled lab environment. We also benchmark representative Full Reference (FR) and No-Reference (NR) objective VQA models against the subjective data to evaluate their performance on compressed UHD-HDR-WCG video content. The database will be made available to the public, subject to content copyright constraints.