**Core Concept**
The suprathyroid artery is responsible for supplying blood to the thyroid gland and surrounding structures. Its ligation or injury can lead to damage to nearby nerves due to anatomical proximity.

**Why the Correct Answer is Right**
The most common nerve injured by ligation of the suprathyroid artery is the External Laryngeal Nerve (ELN). This nerve is a branch of the Superior Laryngeal Nerve, which arises from the Vagus Nerve. The ELN provides motor innervation to the cricothyroid muscle and sensory innervation to the larynx. Due to its close proximity to the suprathyroid artery, injury to the ELN can occur during surgical procedures involving this artery.

**Why Each Wrong Option is Incorrect**
* **Option A:** The Inferior Laryngeal Nerve (also a branch of the Superior Laryngeal Nerve) is not typically injured during ligation of the suprathyroid artery.
* **Option B:** The Recurrent Laryngeal Nerve (RLN), which is a branch of the Vagus Nerve, is not directly related to the suprathyroid artery and is not commonly injured during its ligation.
* **Option C:** The Hypoglossal Nerve is not related to the thyroid gland or the suprathyroid artery and is not typically injured during procedures involving this artery.

**Clinical Pearl / High-Yield Fact**
The External Laryngeal Nerve is at risk during thyroid surgery, particularly during ligation of the suprathyroid artery. Injury to this nerve can result in vocal cord paralysis, which can have significant consequences for the patient's voice and respiratory function.

**Correct Answer:** D.