Background/Objectives: Carbapenem-resistant Klebsiella pneumoniae (CRKP) threatens Intensive Care Units (ICU), particularly in settings where serine (KPC) and metallo-β-lactamases (NDM) co-circulate. The aim of this study was to assess CRKP susceptibility especially to novel β-lactam/β-lactamase inhibitor combinations, characterize the genetic determinants of resistance, and contribute to the understanding of local epidemiology in the ICU of our hospital. Methods: We studied 32 non-duplicate CRKP isolates (30 ICU, 2 wards) collected at Hippokration General Hospital, Thessaloniki (May–Oct 2023). Bacterial identification and Antimicrobial susceptibility testing (AST) were performed by VITEK-2; Minimum inhibitory concentrations (MICs) for ceftazidime/avibactam (CAZ/AVI), meropenem/vaborbactam (MER/VAB), and imipenem/relebactam (IMI/REL) were determined by E-tests. Colistin MICs were performed by broth microdilution. Carbapenemases were screened phenotypically and by immunochromatography and confirmed by multiplex PCR. One bronchial isolate co-harboring bla_NDM and bla_KPC genes underwent WGS. Results: All isolates were carbapenem-resistant and showed extensive resistance to β-lactams and fluoroquinolones. By PCR, 8/32 (25%) carried bla_KPC alone, 8/32 (25.0%) bla_NDM alone, and 16/32 (50%) co-harbored bla_KPC and bla_NDM. KPC-only isolates were generally susceptible in vitro to CAZ/AVI, MER/VAB, and IMI/REL, whereas dual KPC-NDM producers were resistant to all three combinations. Tigecycline showed the highest retained activity; colistin remained active in a minority. WGS of one ST512 (CG258) isolate revealed co-harboring bla_NDM-1 and bla_KPC-3 with additional resistance determinants and plasmid replicons, consistent with high-risk spread. Conclusions: Half of CRKP isolates in this ICU-predominant series co-produced KPC and NDM, severely limiting β-lactam/β-lactamase inhibitor options. These data support routine screening for carbapenemases, strict infection prevention, antimicrobial stewardship, and access to agents active against MBLs.