  We study the process $pp \to Z(\ell^+ \ell^-)h(b\bar b)$ in the Standard
Model Effective Field Theory (SMEFT) at high energies using subjet techniques
to reconstruct the Higgs boson. We show that at high energies this process
probes four directions in the dimension 6 EFT space, namely the operators that
contribute to the four contact interactions, $hZ_\mu \bar{f}\gamma^\mu f$,
where $f=u_L, u_R,d_L$ and $d_R$. These four directions are, however, already
constrained by the $Z$-pole and diboson measurements at LEP. We show that by
utilising the energy growth of this process in the SMEFT and the accuracy that
can be achieved by using subjet techniques at the High Luminosity LHC, one can
obtain bounds on these operators that are an order of magnitude better than
existing LEP bounds.
