We investigate current-driven modes developing at jet fronts during collisionless reconnection. Initial evolution of the reconnection is simulated using conventional 2-D setup starting from the Harris equilibrium. Three-dimensional PIC calculations are implemented at later stages, when fronts are fully formed. Intense currents and enhanced wave activity are generated at the fronts because of the interaction of the fast flow plasma and denser ambient current sheet plasma. The study reveals that the lower hybrid drift instability develops quickly in the 3-D simulation. The instability produces strong localized perpendicular electric fields, which are several times larger than the convective electric field at the front, in agreement with Time History of Events and Macroscale Interactions during Substorms observations. The instability generates waves, which escape the front edge and propagate into the undisturbed plasma ahead of the front. The parallel electron pressure is substantially larger in the 3-D simulation compared to that of the 2-D. In a time similar to Omega(-1)(ci), the instability forms a layer, which contains a mixture of the jet plasma and current sheet plasma. The results confirm that the lower hybrid drift instability is important for the front evolution and electron energization.