Simulations of star cluster formation and evolution are usually divided into the (magneto-)hydrodynamical evolution, and the N-body evolution with separate codes. We present a new hybrid SPH and N-body algorithm designed to bridge the divide between the two classes of simulation. The ballistical motion of the stars is integrated with a 4th-order Hermite integrator, as used in many N-body codes, whereas the background gas is modelled with a low-resolution SPH simulation with a 2nd-order leapfrog integrator. The stars can interact with the gas by gravitational forces and mechanical and radiative feedback processes, thus taking advantage of the various algorithms already implemented into the SPH code. We have implemented our new approach into the SPH code SEREN and we present one simple test case demonstrating the fidelity of the algorithm. We discuss the assumptions and restrictions underlying the method and possible future applications for star cluster research.