Background: Obstructive sleep apnea (OSA) increases the risk of stroke and cardiovascular diseases. However, its impact on geriatric patients with a prior history of stroke/transient ischemic attack (TIA) has not been adequately studied. Methods: We utilized the 2019 National Inpatient Sample in the US to identify geriatric patients with OSA (G-OSA) who had a prior history of stroke/TIA. We then compared subsequent stroke (SS) rates among sex and race subgroups. We also compared the demographics and comorbidities of SS+ and SS− groups and utilized logistic regression models to assess outcomes. Results: Out of 133,545 G-OSA patients admitted with a prior history of stroke/TIA, 4.9% (6520) had SS. Males had a higher prevalence of SS, while Asian-Pacific Islanders and Native Americans had the highest prevalence of SS, followed by Whites, Blacks, and Hispanics. The SS+ group had higher all-cause in-hospital mortality rates, with Hispanics showing the highest rate compared to Whites and Blacks (10.6% vs. 4.9% vs. 4.4%, p < 0.001), respectively. Adjusted analysis for covariates showed that complicated and uncomplicated hypertension (aOR 2.17 [95% CI 1.78–2.64]; 3.18 [95% CI 2.58–3.92]), diabetes with chronic complications (aOR 1.28 [95% CI 1.08–1.51]), hyperlipidemia (aOR 1.24 [95% CI 1.08–1.43]), and thyroid disorders (aOR 1.69 [95% CI 1.14–2.49]) were independent predictors of SS. The SS+ group had fewer routine discharges and higher healthcare costs. Conclusions: Our study shows that about 5% of G-OSA patients with a prior history of stroke/TIA are at risk of hospitalization due to SS, which is associated with higher mortality and healthcare utilization. Complicated and uncomplicated hypertension, diabetes with chronic complications, hyperlipidemia, thyroid disorders, and admission to rural hospitals predict subsequent stroke.