Photoluminescent (PL) gold nanoclusters (AuNCs) show many advantages over conventional semiconductor quantum dots, however, their application potential is limited by their relatively low absorption cross-section and quantum yield. Plasmonic enhancement is a common strategy for improving the performance of weak fluorophores, yet in the case of AuNCs this method is still poorly explored. Here a robust synthetic approach to a compact plasmonic nanostructure enhancing significantly the PL of AuNCs is presented. Two gold nanostructures, AuNCs and plasmonic gold nanorods (AuNRs), are assembled in a compact core-shell nanostructure with tunable geometry and optical properties. The unprecedented degree of control over the structural parameters of the nanostructure allows to study the effects of several parameters, such as excitation wavelength, AuNC-AuNR distance, and relative loading of AuNCs per single AuNR. Consequently, a more general method to measure and evaluate enhancement independently of the absolute particle concentrations is introduced. The highest PL intensity enhancement is obtained when the excitation wavelength matches the strong longitudinal plasmonic band of the AuNRs and when the separation distance between AuNCs and AuNRs decreases to 5 nm. The results presented are relevant for the application of AuNCs in optoelectronic devices and bioimaging.