  We compute lattice renormalisation constants of one-link quark operators
({\it i.e.} operators with one covariant derivative) for overlap fermions and
L\"uscher-Weisz gauge action in one-loop perturbation theory. Among others,
such operators enter the calculation of moments of polarised and unpolarised
hadron structure functions. Results are given for \beta=8.45, \beta=8.0 and
mass parameter \rho=1.4, which are commonly used in numerical simulations. We
apply mean field (tadpole) improvement to our results.
