A new correlation functional is derived within the Kohn-Sham (KS) Density Functional Theory (DFT) involving the electron kinetic energy density tau and the Laplacian of the electron density as key nonlocal variables. The derivation is based on a direct resolution of the adiabatic connection formula and using an analogy with the local thermodynamic approach in DFT, following the Lap3 theory developed previously. Compared to the latter, the new functional involves higher order tau -dependent energy terms in a form suggesting a possible resummation procedure that could be used for further development. It is combined with the nonlocal exchange functional of Becke, by modifying the latter in an empirical fashion to achieve better synchronization between the two energy components. The resulting exchange-correlation scheme (named "Bm tau1") is validated on several test systems known as difficult for DFT, at least at the Local Spin Density and Generalized Gradient Approximation levels. The recent nonempirical hybrid scheme PBE1PBE ("PBE0") is included in the comparative tests as a parameter-free benchmark for the hybrid HF-KS DFT approach. Improved results for relative energies, activation barriers and equilibrium geometries are obtained with the Bm tau1 functional, particularly concerning aromatic compounds, systems with weak hydrogen bonds, proton transfer processes and transition-metal carbonyls.