Objective: This paper aims to prompt large language models (LLMs) for clinical temporal relation extraction (CTRE) in both few-shot and fully supervised settings. Materials and Methods: This study utilizes four LLMs: Encoder-based GatorTron-Base (345M)/Large (8.9B); Decoder-based LLaMA3-8B/MeLLaMA-13B. We developed full (FFT) and parameter-efficient (PEFT) fine-tuning strategies and evaluated these strategies on the 2012 i2b2 CTRE task. We explored four fine-tuning strategies for GatorTron-Base: (1) Standard Fine-Tuning, (2) Hard-Prompting with Unfrozen LLMs, (3) Soft-Prompting with Frozen LLMs, and (4) Low-Rank Adaptation (LoRA) with Frozen LLMs. For GatorTron-Large, we assessed two PEFT strategies-Soft-Prompting and LoRA with Frozen LLMs-leveraging Quantization techniques. Additionally, LLaMA3-8B and MeLLaMA-13B employed two PEFT strategies: LoRA strategy with Quantization (QLoRA) applied to Frozen LLMs using instruction tuning and standard fine-tuning. Results: Under fully supervised settings, Hard-Prompting with Unfrozen GatorTron-Base achieved the highest F1 score (89.54%), surpassing the SOTA model (85.70%) by 3.74%. Additionally, two variants of QLoRA adapted to GatorTron-Large and Standard Fine-Tuning of GatorTron-Base exceeded the SOTA model by 2.36%, 1.88%, and 0.25%, respectively. Decoder-based models with frozen parameters outperformed their Encoder-based counterparts in this setting; however, the trend reversed in few-shot scenarios. Discussions and Conclusions: This study presented new methods that significantly improved CTRE performance, benefiting downstream tasks reliant on CTRE systems. The findings underscore the importance of selecting appropriate models and fine-tuning strategies based on task requirements and data availability. Future work will explore larger models and broader CTRE applications.