For years, frequency standards have been the cornerstone of precision measurement. Among these frequency standards, atomic clocks have set records in both precision and accuracy, and have redefined the second. There is growing interest in more complex molecular systems to complement precision measurements with atoms. The rich internal structure of even the simplest diatomic molecules could provide new avenues for fundamental physics research, including searches for extensions to the Standard Model, dark matter candidates, novel forces or corrections to gravity at short distances, and tests of the variation of fundamental constants. In this thesis, we discuss the fundamental architecture for a precise molecular system based on a strongly forbidden weakly-bound to deeply-bound vibrational transition in 88Sr dimers. We discuss early studies to characterise our system and gain technical and quantum control over the experiment in anticipation of a precise metrological measurement. We, then, demonstrate a record-breaking precision for our 88Sr2 molecular clock ushering in a new era for precision measurement with clocks. Borrowing techniques from previous atomic clock architecture, we measure a ∼32 THz clock transition between two vibrational levels in the electronic ground state, achieving a fractional uncertainty of 4.6 × 10−14 in a new frequency regime. In this current iteration, our molecular clock is fundamentally limited by two-body loss lifetimes of 200 ms and light scattering induced by our high-intensity lattice. Given these limitations, we suggest improvements to combat the effects from both the lattice and two-body collisions in our 1D trap. These include technical improvements to our experiment and strategic choices of particular clock states in our ground electronic potential. We describe in-depth studies of the chemistry and polarizability behaviour of our molecule, which elucidates preferential future directions for a second generation clock system. These empirical results are substantiated by an improved theoretical picture. Ultimately, our molecular system is built in order to probe new physics and as a tool for precision measurement. Leveraging our record-precision clock and our new-found understanding of our molecule, we predict the capacity for our system to place meaningful, competitive constraints on new physics, in particular on Yukawa-type extensions to gravity. These predictions motivate improvements to our current generation clock and set the stage for future measurements with this system.