**Core Concept**
The palatine tonsil receives its blood supply from branches of the external carotid artery, which is a key concept in understanding the vascular anatomy of the head and neck. The external carotid artery gives rise to several branches that supply the tonsils, among other structures.

**Why the Correct Answer is Right**
The palatine tonsil is primarily supplied by the tonsillar branches of the facial artery, which is a branch of the external carotid artery. However, the palatine tonsil also receives a small contribution from the superior thyroid artery, which is another branch of the external carotid artery. The palatine tonsil does not receive significant blood supply from the internal carotid artery, which is a key distinction in this question.

**Why Each Wrong Option is Incorrect**
**Option A:** The tonsillar branches of the facial artery are a primary source of blood supply to the palatine tonsil, making this option incorrect.
**Option B:** The superior thyroid artery does contribute to the blood supply of the palatine tonsil, making this option incorrect.
**Option D:** This option is incomplete and cannot be evaluated as correct or incorrect.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the palatine tonsil receives its blood supply from branches of the external carotid artery, which is distinct from the internal carotid artery. This knowledge is crucial in understanding the vascular anatomy of the head and neck.

**Correct Answer: D.**