Effective operators up to the p^4-order in the Lagrangian expansion are completely listed for both of the CP-conserving and non-conserving cases, in a larger symmetry group SU(2)_L x SU(2)_R x U(1)_{B−L} and within a non-linear electroweak scenario coupled to a light dynamical Higgs. The phenomenology induced by integrating out the right handed fields from the physical spectrum is also analysed. The excess events reported by the ATLAS Collaboration in the WZ-final state, and by the CMS Collaboration in the e^+ e^- jj, Wh and jj-final states, are tackled in the model via decays of a heavy boson W' in the 1.8--2 TeV mass range. A heavy Z' boson with a mass of 2.5–4 TeV is predicted, and some decay channels testable in future colliders are also discussed.