This work studies the stability of the toroidicity-induced Alfvén eigenmodes (TAE) in the proposed ITER burning plasma experiment, which can be driven unstable by two groups of energetic particles, the 3.5 MeV α-particle fusion products and the tangentially injected 1 MeV beam ions. Both species are super-Alfvénic but they have different pitch angle distributions and the drive for the same pressure gradients is typically stronger from co-injected beam ions as compared with the isotropically distributed α-particles. This study includes the effect of anisotropy of the beam ion distribution function on TAE growth rate directly via the additional velocity space drive and indirectly in terms of the enhanced effect of the resonant particle phase space density. For near parallel injection TAEs are marginally unstable if the injection aims at the plasma centre, where the ion Landau damping is strong, whereas with the off-axis neutral beam injection the instability is stronger with the growth rate near 0.5% of the TAE mode frequency. In contrast, for perpendicular beam injection TAEs are predicted to be stabilized in nominal ITER discharges.In addition, the effect of TAEs on the fast ion beta profiles is evaluated by introducing a fast ion redistribution toy model based on a quasi-linear diffusion theory, which uses analytic expressions for the local growth and damping rates. These results illustrate the parameter window that is available for plasma burn when TAE modes are excited.