Ceftazidime/avibactam is an important treatment option for infections caused by Klebsiella pneumoniae carbapenemase-producing K. pneumoniae (KPC-Kp), however, resistance can emerge during treatment. The objective of the study was to define the ceftazidime/avibactam concentrations required to suppress bacterial regrowth in ceftazidime/avibactam susceptible isolates and identify active therapies against ceftazidime/avibactam-resistant KPC-Kp. Time-kill assays were performed against twelve ST258 KPC-Kp isolates that harbored blaKPC–2 or blaKPC–3. Nine KPC-Kp isolates (KPC-Kp 5A, 6A, 7A, 8A, 9A, 24A, 25A, 26A, and 27A) were susceptible to ceftazidime/avibactam, two (KPC-Kp 6B and 7B) were ceftazidime/avibactam resistant and meropenem susceptible, and one (KPC-Kp 1244) was resistant to both ceftazidime/avibactam and meropenem. Sequencing of the blaKPC genes revealed mutations in KPC-Kp 6B (D179Y substitution) and 7B (novel 21 base pair deletion) that both affected the Ω-loop encoding portion of the gene. Time-kill assays showed that against ceftazidime/avibactam-susceptible KPC-Kp, ceftazidime/avibactam concentrations ≥40/7.5 mg/L caused mean 5.42 log10CFU/mL killing and suppressed regrowth. However, regrowth occurred for some KPC-Kp isolates with a ceftazidime/avibactam concentration of 20/3.75 mg/L. Against ceftazidime/avibactam-resistant and meropenem-susceptible KPC-Kp 6B and 7B, bactericidal activity and synergy was observed for ceftazidime/avibactam in combination with meropenem ≤3.125 mg/L, while meropenem concentrations ≥50 mg/L were bactericidal as monotherapy. In contrast, clinically achievable concentrations of ceftazidime/avibactam were bactericidal against KPC-Kp 1244, which was ceftazidime/avibactam-resistant and meropenem-resistant due to outer membrane porin mutations and elevated blaKPC expression. Achieving high ceftazidime/avibactam concentrations may help to suppress bacterial regrowth in the presence of ceftazidime/avibactam. The optimal treatment approach for ceftazidime/avibactam-resistant KPC-Kp likely depends on the mechanism of resistance. Additional studies are warranted to confirm these findings.