This paper discusses the methods that we used for our submissions to the WMT 2023 Terminology Shared Task for German-to-English (DE-EN), English-to-Czech (EN-CS), and Chinese-to-English (ZH-EN) language pairs. The task aims to advance machine translation (MT) by challenging participants to develop systems that accurately translate technical terms, ultimately enhancing communication and understanding in specialised domains. To this end, we conduct experiments that utilise large language models (LLMs) for two purposes: generating synthetic bilingual terminology-based data, and post-editing translations generated by an MT model through incorporating pre-approved terms. Our system employs a four-step process: (i) using an LLM to generate bilingual synthetic data based on the provided terminology, (ii) fine-tuning a generic encoder-decoder MT model, with a mix of the terminology-based synthetic data generated in the first step and a randomly sampled portion of the original generic training data, (iii) generating translations with the fine-tuned MT model, and (iv) finally, leveraging an LLM for terminology-constrained automatic post-editing of the translations that do not include the required terms. The results demonstrate the effectiveness of our proposed approach in improving the integration of pre-approved terms into translations. The number of terms incorporated into the translations of the blind dataset increases from an average of 36.67% with the generic model to an average of 72.88% by the end of the process. In other words, successful utilisation of terms nearly doubles across the three language pairs.