Combining genome assembly with population and functional genomics can provide valuable insights to development and evolution, as well as tools for species management. Here, we present a chromosome-level genome assembly of the common brushtail possum (Trichosurus vulpecula), a model marsupial threatened in parts of their native range in Australia, but also a major introduced pest in New Zealand. Functional genomics reveals post-natal activation of chemosensory and metabolic genes, reflecting unique adaptations to altricial birth and delayed weaning, a hallmark of marsupial development. Nuclear and mitochondrial analyses trace New Zealand possums to distinct Australian subspecies, which have subsequently hybridised. This admixture allowed phasing of parental alleles genome-wide, ultimately revealing at least four genes with imprinted, parent-specific expression not yet detected in other species (MLH1, EPM2AIP1, UBP1 and GPX7). We find that reprogramming of possum germline imprints, and the wider epigenome, is similar to eutherian mammals except onset occurs after birth. Together, this work is useful for genetic-based control and conservation of possums, and contributes to understanding of the evolution of novel mammalian epigenetic traits.