We propose a closed-form (i.e. without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) whenthe massless particle is in an orbit exterior to the one of the primary perturber. Starting with a multipole expansion of the barycentric (Jacobi-reduced) Hamiltonian, we carry out asequence of normalizations in Delaunay variables by Lie series, leading to a secular Hamiltonianmodel without use of relegation. To this end, we introduce a book-keeping analogous tothe one proposed in Cavallari & Efthymiopoulos (2022, CMDA) for test particle orbits interior to the one of the primary perturber, but here adapted, instead, to the case of exterior orbits. We give numerical examples ofthe performance of the method in both the planar circular and the spatial elliptic restrictedthree-body problem, for parameters pertinent to the Sun-Jupiter system. In particular, we demonstrate the method's accuracy in terms of reproducibility of the orbital elements' variations far from mean-motion resonances. As a basic outcome of the method, we show how,using as criterion the size of the series' remainder, we reach to obtain an accurate semianalytical estimate of the boundary (in the space of orbital elements) where the secularHamiltonian model arrived at after eliminating the particle's fast degree of freedom providesa valid approximation of the true dynamics.