The accurate computation of ionization potentials (IPs), within 0.10 eV, is one of the most challenging problems in modern computational chemistry. The extended Koopmans' theorem (EKT) provides a systematic direct approach to compute IPs from any level of theory. In this study, the EKT approach is integrated with the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for the first time. For efficiency, the density-fitting (DF) approximation is employed for electron repulsion integrals. Further, the EKT-CCSD(T) method is applied to a set of 23 molecules, denoted as IP23, for comparison with the experimental ionization potentials. For the IP23 set, the EKT-CCSD(T) method, along with the aug-cc-pV5Z basis set, provides a mean absolute error of 0.05 eV. Hence, our results demonstrate that direct computations of IPs at high-accuracy levels can be achieved with the EKT-CCSD(T) method. We believe that the present study may open new avenues in IP computations.