We report on the studies of Transverse-Momentum-Dependent distributions (TMDs) at a future fixed-target experiment --AFTER@LHC-- using the \(p^+\) or Pb ion LHC beams, which would be the most energetic fixed-target experiment ever performed. AFTER@LHC opens new domains of particle and nuclear physics by complementing collider-mode experiments, in particular those of RHIC and the EIC projects. Both with an extracted beam by a bent crystal or with an internal gas target, the luminosity achieved by AFTER@LHC surpasses that of RHIC by up to 3 orders of magnitude. With an unpolarised target, it allows for measurements of TMDs such as the Boer-Mulders quark distributions and the distribution of unpolarised and linearly polarised gluons in unpolarised protons. Using polarised targets, one can access the quark and gluon Sivers TMDs through single transverse-spin asymmetries in Drell-Yan and quarkonium production. In terms of kinematics, the fixed-target mode combined with a detector covering \(\eta_{\rm lab} \in [1,5]\) allows one to measure these asymmetries at large \(x^\uparrow\) in the polarised nucleon.