Although previous studies have identified human-specific accelerated regions as playing a key role in the recent evolution of the human brain, the characteristics and cellular functions of rapidly evolving conserved elements (RECEs) in ancestral primate lineages remain largely unexplored. Here, based on large-scale primate genome assemblies, we identify 888 RECEs that have been highly conserved in primates that exhibit significantly accelerated substitution rates in the ancestor of the Simiiformes. This primate lineage exhibits remarkable morphological innovations, including an expanded brain mass. Integrative multiomic analyses reveal that RECEs harbor sequences with potential cis-regulatory functions that are activated in the adult human brain. Importantly, genes linked to RECEs exhibit pronounced expression trajectories in the adult brain relative to the fetal stage. Furthermore, we observed an increase in the chromatin accessibility of RECEs in oligodendrocytes from individuals with Alzheimer's disease (AD) compared to that of a control group, indicating that these RECEs may contribute to brain aging and AD. Our findings serve to expand our knowledge of the genetic underpinnings of brain function during primate evolution.