Physical realizations of quantum computers in the current era greatly vary in multiple, non-trivial aspects. A fundamental difference between two hardware realizations of a quantum computer can be the choice of implementation of their qubits. Current candidates for qubit implementations are superconducting qubits, trapped ions, nitrogen-vacancy centers, and neutral atoms, to name a few. Each choice of qubit implementation comes with distinct features that need to be considered when compiling and synthesizing circuits for a quantum computer based on them. For instance, the connectivity between qubits in a superconducting quantum computer is limited to a connectivity graph that depends on a specific topology, while on a trapped ion quantum computer, the connectivity is all-to-all. This all-to-all connectivity naturally gives us a special set of quantum gates to work with, in which we have access to powerful multi-qubit entangling gates that we refer to as global gates. So, to effectively use ion-trap quantum computers, we need quantum circuit synthesis that takes advantage of the global gates. In this work, we describe and implement an algorithm that converts any input quantum circuit into one that uses the gate set native to ion trap quantum platforms. Our synthesis algorithm is based on the ZX-calculus and consists of a circuit extraction procedure that outputs a circuit with global entangling gates and arbitrary single-qubit gates. In the process, we minimize the number of synthesized global gates since they are the dominating factor contributing to circuit runtime.