We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \bar psi sigma_mu nu psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p2). With this choice, we build the even-parity effective Lagrangian up to the p6-order (NLO). While there are only 4 new terms at the p4-order, at p6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p8-order (NNLO).