Training data is fundamental to the success of modern machine learning models, yet in high-stakes domains such as healthcare, the use of real-world training data is severely constrained by concerns over privacy leakage. A promising solution to this challenge is the use of differentially private (DP) synthetic data, which offers formal privacy guarantees while maintaining data utility. However, striking the right balance between privacy protection and utility remains challenging in clinical note synthesis, given its domain specificity and the complexity of long-form text generation. In this paper, we present Term2Note, a methodology to synthesise long clinical notes under strong DP constraints. By structurally separating content and form, Term2Note generates section-wise note content conditioned on DP medical terms, with each governed by separate DP constraints. A DP quality maximiser further enhances synthetic notes by selecting high-quality outputs. Experimental results show that Term2Note produces synthetic notes with statistical properties closely aligned with real clinical notes, demonstrating strong fidelity. In addition, multi-label classification models trained on these synthetic notes perform comparably to those trained on real data, confirming their high utility. Compared to existing DP text generation baselines, Term2Note achieves substantial improvements in both fidelity and utility while operating under fewer assumptions, suggesting its potential as a viable privacy-preserving alternative to using sensitive clinical notes.