The outer membrane of Gram-negative bacteria constitutes a permeability barrier that prevents certain antibiotics reaching their target, thus conferring a high tolerance to a wide range of antibiotics. Combined therapies of antibiotics and outer membrane-perturbing drugs have been proposed as an alternative treatment to extend the use of antibiotics active against Gram-positive bacteria to Gram-negative bacteria. Among the outer membrane-active compounds, the outer membrane-permeabilising peptides play a prominent role. They form a group of small cationic and amphipathic molecules with the ability to insert specifically into bacterial membranes, inducing their permeabilisation and/or disruption. Here we assessed the combined effect of several compounds belonging to the main antibiotic families and the cathelicidin close-to-nature outer membrane peptide D-11 against four clinically relevant Gram-negative bacteria. The results showed that peptide D-11 displays strong synergistic activity with several antibiotics belonging to different families, in particular against Klebsiella pneumoniae, even better than some other outer membrane-active peptides that are currently in clinical trials, such as SPR741. Notably, we observed this activity in vitro, ex vivo in a newly designed bacteraemia model, and in vivo in a mouse abscess infection model. Overall, our results suggest that D-11 is a good candidate to repurpose the activity of traditional antibiotics against K. pneumoniae.