We review a number of ideas put forward in favour of the use of a polarised target along with the proposed idea of a fixed-target experiment using the LHC beams -- AFTER@LHC. A number of recent studies have shown that single transverse-spin asymmetries (STSAs) are large enough to be precisely measured in the region accessible with AFTER@LHC, in particular as regards the Drell-Yan process as well as single-pion, isolated-photon and jet production. AFTER@LHC with a polarised target would also be the ideal experimental set-up to measure the gluon Sivers effect via a number of original quarkonium STSA studies. We discuss first figures-of-merit based on simulations for AFTER@LHC with a polarised target. Show Partial Abstract