The Metric Coalescent is a measure-valued Markov process defined over any metric space $(S, d)$, starting from any finitely supported initial measure $\mu \in \mathfrak{P}(S)$. In this talk we will show that for a compact Polish space, the MC process can be uniquely extended to all of $\mathfrak{P}(S)$, following an approach reminiscent of exchangeable, coalescent random partitions.