Cardiovascular diseases, especially hypertension, stand as prominent contributors to global mortality. Hypertension, often referred to as a silent killer syndrome, necessitates the use of multiple medications for effective control and management. A new environmentally friendly HPLC–DAD method is introduced in this study for the concurrent analysis of telmisartan (TEL), chlorthalidone (CHT) and amlodipine besylate (AML), in both pure forms and combined pharmaceutical dosage form. An isocratic elution mode was employed to achieve chromatographic separation, utilizing an Inertsil C18 column (250 × 4.6 mm, 5.0 µm) and a mobile phase mixture of acetonitrile and phosphate buffer (pH 3.0 ± 0.1) with ratio of 35:65, v/v. The separation was achieved within 10 min at a flow rate of 1.0 mL/min. The proposed method's validation was carried out following the guidelines outlined by the International Council for Harmonisation (ICH). The achieved linearity range was 1.0–140.0 μg/mL for TEL and 1.0–100.0 μg/mL for CHT and AML with quantification limits of 0.061, 0.177, and 0.313 μg/mL for TEL, CHT, and AML, respectively. The fixed combination tablet dosage form demonstrated acceptable release profile, as indicated by the in-vitro dissolution studies. The studied dissolution media were phosphate buffer pH 7.5, 0.01 N HCl, and water, utilizing a USP type II apparatus at 37 ± 0.5 °C with a stirring rate of 75 rpm. The proposed method was applied successfully for the quality assessment of Telma-ACT® Tablets with good precision and accuracy. Various tools were used for evaluating the level of greenness, including Green Analytical Procedure Index (GAPI), Analytical Greenness Metric for Sample Preparation (AGREEprep), Analytical Eco-Scale (AES), and Analytical Method Greenness Score (AMGS). These tools had confirmed the eco-friendliness of the proposed method. Additionally, the newly introduced White Analytical Chemistry (WAC), and the Blue Applicability Grade Index (BAGI) have been specifically developed to evaluate the sustainability and the applicability of the method.