This work describes the development of a gamma detector based on silicon drift detectors (SDDs) to read out large ${\hbox{LaBr}}_3$ : ${\hbox{Ce}}$ scintillators for gamma-ray astronomy applications, within an activity supported by the European Space Agency (ESA). SDDs, characterized by high quantum efficiency and low electronic noise, when coupled with a scintillator are good candidates for gamma-ray spectroscopy applications in a wide energy range, e.g., from 150 keV to 15 MeV. The gamma-ray detector prototype presented here is composed of a 2 ${^\prime}{^\prime}$ $\times$ 2 ${^\prime}{^\prime}$ ${\hbox{LaBr}}_3$ : ${\hbox{Ce}}$ scintillator coupled with four SDD arrays arranged in a $2 \times 2$ format (a total of 36 SDDs). This detection system is operated with custom readout application specific integrated circuits (ASICs) and a data acquisition (DAQ) system. With this prototype gamma-camera, an energy resolution of 3.4% FWHM at 662 keV has been measured. Spectroscopy measurements have been carried out between 300 keV and 1800 keV and the achieved results are consistent with the electronic noise of the SDD technology. In this work, we report on the SDD based detection head’s design, its X-ray characterization, readout electronics, experimental setups and gamma-ray spectroscopy results. Finally, perspectives with the possible use of an improved SDD technology are discussed.