The first search is presented for vector-like leptons (VLLs) in the context of the “4321 model”, an ultraviolet-complete model with the potential to explain existing B physics measurements that are in tension with standard model predictions. The analyzed data, corresponding to an integrated luminosity of 96.5fb−1, were recorded in 2017 and 2018 with the CMS detector at the LHC in proton-proton collisions at s=13TeV. Final states with ≥3 b -tagged jets and two third-generation leptons (ττ, τντ, or ντντ) are considered. Upper limits are derived on the VLL production cross section in the VLL mass range 500–1050 GeV. The maximum likelihood fit prefers the presence of signal at the level of 2.8 standard deviations, for a representative VLL mass point of 600 GeV. As a consequence, the observed upper limits are approximately double the expected limits.