Cold dark matter in the form of weakly interacting massive particles (WIMPs) is a favoured explanation to the galactic dark matter puzzle and could account for a large proportion of the missing mass of the Universe. There are currently numerous detectors around the world attempting to observe a WIMP signal. The ZEPLIN-III detector is one such device. Utilising liquid xenon as a target medium, identification is based on extraction of scintillation and electroluminescence signals from the two-phase xenon target caused when WIMPs scatter and has recently completed its first science run (FSR). With no WIMP signal observed, ZEPLIN-III has excluded a WIMP-nucleon spin-independent cross section above 8.1 × 10−8 pb (90% confidence limit) for a WIMP mass of 60 GeV/c2 and also set a 90% confidence upper limit of a pure WIMP-neutron spin-dependent cross section of 1.9 × 10−2 pb for a 55 GeV/c2 WIMP mass. However, the focus of this thesis is the future of the ZEPLIN-III detector with regards to the second science run (SSR). As with all dark matter detectors, background reduction from neutrons and gamma-rays plays a significant part in obtaining competitive WIMP detection sensitivities. The author has contributed significantly to the design, development and testing of a low radioactivity veto for the ZEPLIN-III detector, to be retrofitted in time for the SSR. It will detect neutrons and gamma-rays in coincidence with the ZEPLIN-III target allowing these events to be removed as candidate WIMP events. This thesis describes the author’s contribution to the design, construction, testing and evaluation of the veto. Also discussed is the development of a comprehensive Monte Carlo simulation, utilised to aid in the design process, to determine the background rates emanating from the veto components (and therefore possible impact on the low sensitivity running of ZEPLIN-III), and to provide an accurate estimation of the overall veto efficiency to reject coincident neutrons and gamma-rays. The veto will have a neutron rejection factor of 67%, reducing the expected neutron background in ZEPLIN-III from 0.4 neutrons/year to 0.14 neutrons/year, a significant factor in the event of a possible WIMP observation. In addition to the work performed on the ZEPLIN-III veto, the author has also contributed to the first science run analysis program by profiling the historical evolution of the electron lifetime throughout the FSR, and implementing consideration of this to improve the data quality.