In this work, the coupling among several MHD modes across different spatial regions, including the neoclassical tearing mode (NTM) and two branches of Alfvén eigenmode (AE) in the core and the edge localized mode (ELM), has been investigated in the HL-2A high beta H-mode plasmas. The NTMs induce a saturated m/n=1/1 helical core (m and n are the poloidal and toroidal mode numbers, respectively) through the ”magnetic-flux pumping” effect. The ELM crash results in a rapid (< 1 ms) decrease of the NTM island width followed by a much slower recovery. The degree of the island-width drop is proportional to the normalized beta as well as the ELM size, and can be up to 60%. In addition, two branches of AEs, in the toroidal Alfvén eigenmode (TAE) and beta-induced Alfvén eigenmode (BAE) bands, become evident after the 2/1 NTM onset and their magnitudes are modulated by the 2/1 NTM rotation. Besides, the changes of the TAE and BAE amplitudes are closely related to the temporal evolution of the ELM crash event, implying the strong interaction between AEs and the ELM. It is found that the coupling among these MHD modes in the core region during the NTM phase regulates the edge transport, i.e., relaxation of the pressure profiles, mitigation of the peeling-ballooning instability, reduction of the radial electric field shear and enhancement of the turbulent transport in the pedestal region.