While essential hypertension (HTN) is very prevalent, pulmonary arterial hypertension (PAH) is very rare in the general population. However, due to progressive heart failure, prognoses and survival rates are much worse in PAH. Patients with PAH are at a higher risk of developing supraventricular arrhythmias and malignant ventricular arrhythmias. The latter underlie sudden cardiac death regardless of the mechanical cardiac dysfunction. Systemic chronic inflammation and oxidative stress are causal factors that increase the risk of the occurrence of cardiac arrhythmias in hypertension. These stressful factors contribute to endothelial dysfunction and arterial pressure overload, resulting in the development of cardiac pro-arrhythmic conditions, including myocardial structural, ion channel and connexin43 (Cx43) channel remodeling and their dysfunction. Myocardial fibrosis appears to be a crucial proarrhythmic substrate linked with myocardial electrical instability due to the downregulation and abnormal topology of electrical coupling protein Cx43. Furthermore, these conditions promote ventricular mechanical dysfunction and heart failure. The treatment algorithm in HTN is superior to PAH, likely due to the paucity of comprehensive pathomechanisms and causal factors for a multitargeted approach in PAH. The intention of this review is to provide information regarding the role of Cx43 in the development of cardiac arrhythmias in hypertensive heart disease. Furthermore, information on the progress of therapy in terms of its cardioprotective and potentially antiarrhythmic effects is included. Specifically, the benefits of sodium glucose co-transporter inhibitors (SGLT2i), as well as sotatercept, pirfenidone, ranolazine, nintedanib, mirabegron and melatonin are discussed. Discovering novel therapeutic and antiarrhythmic strategies may be challenging for further research. Undoubtedly, such research should include protection of the heart from inflammation and oxidative stress, as these are primary pro-arrhythmic factors that jeopardize cardiac Cx43 homeostasis, the integrity of intercalated disk and extracellular matrix, and, thereby, heart function.