The Deep State is the entrenched bureaucracy of government and entwined private sector interests.
All the bureaucrats that run the systems of government and remain ensconced in government regardless of elected officials and their relationships with private sector interests.
Think of a complex military program that takes decades to plan and execute, continues on and on from one political administration to another, costing billions.
Example: the Cold War, post 9-11 military interventions, nuclear power, oil dependence, Big Pharma, Wall Street, etc.