Membrane permeability is a natural defense barrier that contributes to increased bacterial drug resistance, particularly for Gram-negative pathogens. As such, accurate delivery of the antibacterial agent to the target has become a growing research area in the infectious diseases field as a means of improving drug efficacy. Although the efficient transport of siderophore-antibiotic conjugates into the cytosol still remains challenging, great success has been achieved in the delivery of β-lactam antibiotics into the periplasmic space via bacterial iron uptake pathways. Cefiderocol, the first siderophore-cephalosporin conjugate approved by the US Food and Drug Administration, is a good example. These conjugation strategies have also been applied to the precise delivery of β-lactamase inhibitors, such as penicillin-based sulfone 1, to restore β-lactam antibiotic efficacy in multidrug-resistant bacteria. Herein, we have explored the impact on the bacterial activity of 1 by modifying its iron chelator moiety. A set of derivatives functionalized with diverse iron chelator groups and linkages to the scaffold (compounds 2-8) were synthesized and assayed in vitro. The results on the ability of derivatives 2-8 to recover β-lactam antibiotic efficacy in difficult-to-treat pathogens that produce various β-lactamase enzymes, along with kinetic studies with the isolated enzymes, allowed us to identify compound 2, a novel β-lactamase inhibitor with an expanded spectrum of activity. Molecular dynamics simulation studies provided us with further information regarding the molecular basis of the relative inhibitory properties of the most relevant compound described herein.