  The $P_5'$ anomaly uncovered by the LHCb experiment in $B \to K^*\mu\mu$
angular observables has motivated a possible $Z'$ boson that couples to
left-handed $b \to s$ transitions, where a model would be gauged $L_\mu -
L_\tau$ symmetry, but direct search for such a $Z'$ is not promising. Less
constrained is an analogous $Z'$ coupling to right-handed $t \to c$
transitions. Motivated by this, we study $cg \to tZ'$ associated production at
LHC, both for a generic model, and in $L_\mu - L_\tau$ with a vector-like U
quark. We also study $c\bar c \to Z'$ production that exists within the model.
Both processes can be probed already with LHC Run 2 data, all the way up to the
HL-LHC with discovery potential.
