"Deep State" is roughly a dog-whistle for the complex system of shadow government that rules all of the "western" countries, and regularly sponsors regime-change operations to install puppet governments elsewhere.

In the USA, the player with by far the most resources and the most aggressive plans in play is the CIA.

CIA personnel are all over the mainstream media, a phenomenon that was formally arranged through a series of dinner parties hosted by Katherine and Philip Graham, who during their lives owned the Washington Post. CNN appears to be a wholely-controlled media asset of the CIA. With his many connections to the New World Order, it's likely that the founder, Ted Turner, has some connection to the CIA.

In the UK, the equivalent organizations are MI5 (domestic matters) and MI6 (foreign operations).

The larger networks that these organizations are part of include the Comittee on Foreign Relations (CFR, which effectively runs the state department from outside the nominal government), the UN and the regional de facto governments (EU, NAFTA, ASEAN, etc), a financial network that includes the central banks (Federal Reserve, Bank of England) and the investment banks, and numerous so-called NGOs (ostensibly "non-governmental organizations", but in reality, fronts for spying and black ops).