Toroidal Alfv\'en eigenmodes (TAEs) can transport fusion-born energetic particles out of the plasma volume, thereby decreasing plasma self-heating efficiency and possibly damaging reactor walls. Therefore, understanding TAE destabilisation and identifying saturation mechanisms is crucial to achieving burning plasma. While TAEs have been studies extensively in the past using kinetic-MHD codes, here a fully gyrokinetic study is employed which allows for additional physics. In the case studied, the primary drive mechanism is identified as the resonance between the magnetic drifts and the TAE, and this is seen to be disrupted by equilibrium flow shear which can stabilize the mode by rotating it in the the poloidal plane. It is found that zonal flows do not play a significant role in the saturation of these TAEs, and there are no saturation mechanisms present in the local gyrokinetic picture that are able to saturate the mode at physically relevant transport levels in the case of TAE-only turbulence. Instead, we confirm that the global profile flattening of fast-ion density is the key saturation mechanism. The nonlinear excitation of TAE travelling along the electron diamagnetic direction and its beating with the ion diamagnetic TAE, resulting in large amplitude oscillations that may help detect TAEs more easily in tokamaks, is also reported.