Bureaucrats do not have the ability to grant further levels of access (they cannot promote to oversighter or checkuser). These capabilities are held only by stewards, a small multilingual group that serves all Wikimedia projects. Stewards are elected annually; for more information, see Steward requests/Permissions.
No objections are raised in 24 hours after he or she nominates themselves at Meta:Requests for adminship. If objections are raised, a short discussion should ensue, at which point after 48 hours an uninvolved bureaucrat will close it and analyse whether consensus believes the concerns are valid or not. If the concerns are considered valid by consensus, the candidate must nominate himself via a one-week RfB process identical to RfA and pass to become a bureaucrat.