A very few cases exist where there is hypertension in people without insulin resistance or hyperinsulinemia primarily from secondary causes.

Based on my searches, I found that research shows the vast majority of hypertension cases are associated with insulin resistance. However, I can identify a few specific categories where hypertension occurs without insulin resistance:

Categories of Hypertension without Insulin Resistance

Category 1: Secondary Hypertension 
The four rare causes we already discussed (Primary Hyperaldosteronism, Pheochromocytoma, Renovascular Hypertension, and Coarctation of the Aorta) represent hypertension without insulin resistance https://pmc.ncbi.nlm.nih.gov/articles/PMC7219403/.
Key Study: https://pubmed.ncbi.nlm.nih.gov/1736930/
Summary: In many forms of secondary hypertension not associated with obesity, such as renovascular or mineralocorticoid hypertension, there is no evidence of insulin resistance. These represent anatomical or hormonal causes of hypertension completely independent of metabolic dysfunction.

Category 2: Salt-Resistant Essential Hypertension
Study: Salt-Sensitivity and Insulin Resistance
PubMed: https://pubmed.ncbi.nlm.nih.gov/24140089/ (PMC: https://pmc.ncbi.nlm.nih.gov/articles/PMC3996172/)
Summary: Essential hypertensive patients with salt-resistance are less insulin resistant than those with salt-sensitivity, and high salt diet impairs insulin sensitivity only in hypertensive patients with salt-sensitivity but not in those with salt-resistance. This suggests a subgroup of hypertensive patients whose blood pressure responds to mechanisms other than insulin resistance.

Category 3: Hypertension Caused By Insulin Sensitivity (Paradoxical)
Study: Insulin Resistance, Hyperinsulinemia, and Blood Pressure
PubMed: https://pubmed.ncbi.nlm.nih.gov/8339937/
Summary: Increases in plasma insulin concentration in the low-normal range were associated with relatively large blood pressure increments in subjects with normal-high insulin sensitivity but not in insulin-resistant subjects https://www.ahajournals.org/doi/10.1161/01.HYP.30.5.1144. This paradoxical finding suggests that in some insulin-sensitive individuals, even normal insulin levels can raise blood pressure through enhanced sodium retention and sympathetic activation.

Important Note:
The research consistently shows that these are MINORITY cases. In primary hypertension, the incidence of insulin resistance and hyperinsulinemia is much higher than in normotensive controls, however not all reported studies show a relationship between hyperinsulinemia and blood pressure elevation. https://pubmed.ncbi.nlm.nih.gov/7898093/

The key finding is that while insulin resistance accounts for the vast majority of essential hypertension cases (especially in the over-50 population), there remain small subsets where other mechanisms predominate—primarily secondary causes and specific genetic/physiological variations in salt handling and sympathetic nervous system response.