**Core Concept**
The patient's symptoms, such as weight loss, increased appetite, sweating, palpitations, and tremors, are suggestive of hyperthyroidism, a condition characterized by an overproduction of thyroid hormones. The thyroid gland plays a crucial role in regulating metabolism, and its dysfunction can lead to various systemic effects.

**Why the Correct Answer is Right**
The best investigation for the clinical diagnosis of hyperthyroidism is a **Thyroid-Stimulating Hormone (TSH) assay**. This test measures the level of TSH, a hormone produced by the pituitary gland that regulates thyroid function. In hyperthyroidism, the TSH level is typically decreased due to negative feedback from excessive thyroid hormones. The TSH assay is a sensitive and specific test for diagnosing hyperthyroidism and can be used to differentiate it from other thyroid disorders, such as hypothyroidism.

**Why Each Wrong Option is Incorrect**
**Option A:** Free thyroxine (FT4) and free triiodothyronine (FT3) assays measure the levels of thyroid hormones in the blood but are not the best initial investigation for diagnosing hyperthyroidism.
**Option B:** Thyroid peroxidase (TPO) antibodies are used to diagnose autoimmune thyroiditis, such as Hashimoto's thyroiditis, but are not the best investigation for hyperthyroidism.
**Option C:** Ultrasound of the thyroid gland can be used to evaluate thyroid gland size and structure but is not the best investigation for diagnosing hyperthyroidism.

**Clinical Pearl / High-Yield Fact**
It's essential to note that a normal TSH level does not rule out hyperthyroidism, especially in patients with subclinical hyperthyroidism. In such cases, measuring FT4 and FT3 levels can be helpful.

**Correct Answer:** D. TSH assay