Acinetobacter baumannii is a common causative agent of hospital-acquired infections and a leading cause of infection in burns patients. Carbapenem-resistant A. baumannii is considered a major public-health threat and has been identified by the World Health Organization as the top priority organism requiring new antimicrobials. The most common mechanism for carbapenem resistance in A. baumannii is via horizontal acquisition of carbapenemase genes. In this study, we sampled 20 A. baumannii isolates from a patient with extensive burns, and characterized the evolution of carbapenem resistance over a 45 day period via Illumina and Oxford Nanopore sequencing. All isolates were multidrug resistant, carrying two genomic islands that harboured several antibiotic-resistance genes. Most isolates were genetically identical and represented a single founder genotype. We identified three novel non-synonymous substitutions associated with meropenem resistance: F136L and G288S in AdeB (part of the AdeABC efflux pump) associated with an increase in meropenem MIC to ≥8 µg ml-1; and A515V in FtsI (PBP3, a penicillin-binding protein) associated with a further increase in MIC to 32 µg ml-1. Structural modelling of AdeB and FtsI showed that these mutations affected their drug-binding sites and revealed mechanisms for meropenem resistance. Notably, one of the adeB mutations arose prior to meropenem therapy but following ciprofloxacin therapy, suggesting exposure to one drug whose resistance is mediated by the efflux pump can induce collateral resistance to other drugs to which the bacterium has not yet been exposed.