The dynamic behaviour of the partially premixed, swirl-stabilised PRECCINSTA gas turbine model combustor is studied using a fully compressible large eddy simulation solver with a 15-step and 19 species reduced methane mechanism. The solver applies a transported sub-grid probability density function approach solved by the Eulerian stochastic fields method to allow for a burning regime independent description of turbulent flames. A specific operating condition prone to self-excited thermo-acoustic and hydrodynamic instabilities is targeted to evaluate the predictive capabilities of the computational method. Excellent agreement with experimental data is obtained for the predicted thermo-acoustic mode representing a pronounced limit-cycle oscillation at the correct frequency and amplitude. Moreover, the periodic formation and suppression of a precessing vortex core is identified as well as periodic shedding of toroidal vortices at the burner nozzle rim. Both phenomena are shown to be directly coupled to the dominant thermo-acoustic mode and their respective interaction with the flame is investigated in further detail.