Transformer models are the state-of-the-art in Natural Language Processing (NLP) and the core of the Large Language Models (LLMs). We propose a transformer-based model for transition-based dependency parsing of free word order languages. We have performed experiments on five treebanks from the Universal Dependencies (UD) dataset version 2.12. Our experiments show that a transformer model, trained with the dynamic word embeddings performs better than a multilayer perceptron trained on the state-of-the-art static word embeddings even if the dynamic word embeddings have a vocabulary size ten times smaller than the static word embeddings. The results show that the transformer trained on dynamic word embeddings achieves an unlabelled attachment score (UAS) of 84.17% for Urdu language which is ≈3.6% and ≈ 1.9% higher than the UAS scores of 80.56857% and 82.26859% achieved by the multilayer perceptron (MLP) using two static state-of-the-art word embeddings. The proposed approach is investigated for Arabic, Persian and Uyghur languages, in addition to Urdu, for UAS scores and the results suggest that the proposed solution outperform the MLP-based approaches.