A search is presented for the lepton flavour violating decay $B+\to K+\mu -\tau +$ using a sample of proton--proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, collected with the LHCb detector and corresponding to a total integrated luminosity of 9 fb$-1$. The $\tau$ leptons are selected inclusively, primarily via decays with a single charged particle. The four-momentum of the $\tau$ lepton is determined by using $B+$ mesons from $Bs2\ast 0\to B+K-$ decays. No significant excess is observed, and an upper limit is set on the branching fraction at 90% confidence level. The obtained limit is comparable to the world-best limit.