Cognitive decline is common among older individuals, and although the underlying brain mechanisms are not entirely understood, researchers have suggested using EEG frontal alpha activity during general anaesthesia as a potential biomarker for cognitive decline. This is because frontal alpha activity associated with GABAergic general anaesthetics has been linked to cognitive function. However, oscillatory-specific alpha power has also been linked with chronological age. We hypothesize that cognitive function mediates the association between chronological age and (oscillatory-specific) alpha power. We analysed data from 380 participants (aged over 60) with baseline screening assessments and intraoperative EEG. We utilized the telephonic Montreal Cognitive Assessment to assess cognitive function. We computed total band power, oscillatory-specific alpha power, and aperiodics to measure anaesthesia-induced alpha activity. To test our mediation hypotheses, we employed structural equation modelling. Pairwise correlations between age, cognitive function and alpha activity were significant. Cognitive function mediated the association between age and classical alpha power [age → cognitive function → classical alpha; β = -0.0168 (95% confidence interval: -0.0313 to -0.00521); P = 0.0016] as well as the association between age and oscillatory-specific alpha power [age → cognitive function → oscillatory-specific alpha power; β = -0.00711 (95% confidence interval: -0.0154 to -0.000842); P = 0.028]. However, cognitive function did not mediate the association between age and aperiodic activity (1/f slope, P = 0.43; offset, P = 0.0996). This study is expected to provide valuable insights for anaesthesiologists, enabling them to make informed inferences about a patient's age and cognitive function from an analysis of anaesthetic-induced EEG signals in the operating room. To ensure generalizability, further studies across different populations are needed.