A Triple-foil differential Plunger for Exotic Nuclei (TPEN) has been developed to measure the lifetimes of excited states in nuclei with small production cross sections. TPEN utilises one target foil and two degrader foils to make differential lifetime measurements by directly determining the decay function and its derivative at a single plunger distance setting. The direct measurement of the decay function and its derivative removes the requirement to measure gamma-ray intensities at several target-to-degrader distances, thereby reducing the beam-time required relative to a conventional plunger with a single-degrader foil. This thesis describes the construction and subsequent commissioning of TPEN with the lifetime measurement of the first excited 4+ state in 156Dy using this differential lifetime technique. The 46(2) ps measured lifetime of the 4+ was found to be in good agreement with the 45.6(5) ps deduced from a previous high-statistics experiment using a conventional two-foil plunger. A comparison between the present work with TPEN and using conventional two-foil plungers reveals that TPEN achieves the same statistical accuracy with a 4-fold reduction in beamtime with this particular 24Mg(136Xe,4n) reaction. TPEN therefore opens up new opportunities to study exotic nuclei with lower production cross sections that were previously inaccessible.