**Core Concept**
The immediate management of a patient developing airway compromise after thyroid surgery involves addressing potential bleeding from the surgical site, which can lead to swelling and compression of the airway. This is a critical situation requiring prompt action to ensure the patient's airway remains patent.

**Why the Correct Answer is Right**
The correct answer is to open the wound sutures in the ward. This is because the patient may be experiencing bleeding from the thyroid bed, which can lead to rapid swelling and airway compromise. Opening the wound sutures allows for immediate assessment of the bleeding site and possible control of the bleeding, thereby preventing further airway compromise. This is a critical step in the management of a patient with suspected bleeding after thyroid surgery.

**Why Each Wrong Option is Incorrect**
**Option A:** Epinephrine injection is not the immediate management for bleeding after thyroid surgery. While epinephrine can be used to control bleeding, it is not the first step in managing a patient with suspected bleeding after thyroid surgery.

**Option B:** Tracheostomy may be necessary if the patient's airway is compromised and cannot be secured with other measures. However, it is not the immediate management for a patient with suspected bleeding after thyroid surgery.

**Option C:** IV calcium gluconate is used to treat hypocalcemia, which can occur after thyroid surgery due to damage to the parathyroid glands. However, it is not the immediate management for a patient with suspected bleeding after thyroid surgery.

**Clinical Pearl / High-Yield Fact**
In cases of suspected bleeding after thyroid surgery, it is essential to prioritize the patient's airway, breathing, and circulation (ABCs). Opening the wound sutures in the ward is a critical step in assessing and controlling potential bleeding, which can lead to airway compromise.

**✓ Correct Answer: D. Open the wound sutures in the ward.**