Hypertension

This is a good question, as this scenario is not uncommon in general
practice. However, while Conn's syndrome is compatible with this patient's
story, I am not sure that it is the most likely cause of his hypertension.
Even assuming he is compliant with his prescribed medications, the
likeliest diagnosis would be essential hypertension, chiefly because it is
by far the commonest cause overall.

Although low, a serum K of 3.4 mmol/L is not strikingly abnormal and
there is ample room to increase the calcium channel blocker and beta
blocker, As such his hypertension is not necessarily difficult to control.

Non-functioning adrenal adenomas are more common than aldosterone
producing adenomas, which makes adrenal imaging an unattractive
investigation. If the peripheral renin:angiotensin ratio is compatible
with Conn's syndrome (and if Conn's syndrome is present), renal vein
sampling for aldosterone would be a better way to lateralise the adenoma
if surgery would be contemplated.

In practice, medical treatment with spironolactone along with
additional antihypertensives if needed will often be sufficient to control
the blood pressure and avoid surgical intervention.

Renal artery stenosis (RAS) would only be expected to be associated
with impaired renal function if the condition is bilateral (or in a single
functioning kidney) and the GFR is angiotensin II dependent, which is not
the case in the majority of patients with RAS even in the older patient
with bilateral atherosclerotic renovascular disease.

As has been noted in the past, a common condition with an uncommon
presentation is still more likely than an uncommon condition with the same
presentation.