A theory for the transport of a tracer in flow dominated by turbulence and jets is developed and tested. Such a system can be taken as a model either for the stirring of true tracers in the atmosphere and ocean, or, less obviously, for the stirring of baroclinic potential vorticity by non-zonal flow in the ocean. The flow is generated by two-dimensional turbulence with a mean vorticity gradient ($\beta$) and forced randomly and isotropically at small scales. The tracer transported by the flow is forced by a mean tracer gradient that is arbitrarily oriented with respect to the mean vorticity gradient. Such a tracer can be decomposed into two independent tracers: one forced by a gradient that is parallel to the vorticity gradient (and so is stirred across jets), and another that is forced by a mean gradient that is perpendicular to the mean vorticity gradient (and so is stirred along jets). The turbulent transport of the tracer across jets has been discussed in previous research, and is well-described by mixing-length theory. Here it is shown that the transport of the tracer along the jets is described by shear dispersion, but with a diffusivity determined by the across-jet mixing. Even at only moderate levels of anisotropy, the along-jet transport is much larger than the corresponding across-jet transport, consistent, for example, with observations from surface floats in the Pacific.