Like others, I found that the first term to come to mind was 'cabal'. Bearing in mind your starting-with-S criterion, however, I tried 'secret cabal' -- but although that expression is sometimes used, it seems essentially tautological.
Staying with S, then, and thinking more closely about films, the expression that I suggest is Star Chamber.
A modern Star Chamber would be (or is imagined as!) a hermetic subgroup of any administrative authority, including governments. The concept is essentially conspiratorial: a small group routinely operating without hindrance by its own organisation's published ethical principles and procedures. It is in the nature of a Star Chamber that while some might suspect its existence (perhaps following a surprising coincidence of assassinations or commercial deals), we can never find the evidence to prove it.
The general idea in practice is that, however open and democratic the organisation might be thought to be (and might broadly think itself to be), this small assembly of senior individuals is the group that actually takes all of the important policy, strategic and tactical decisions.
The remaining governance structure is unaware of the Star Chamber, and is there for two main reasons. The legitimate structure of departments and so on provides a superficial public image of fairness, conscience and judiciousness; and it controls the infrastructure that in fact enacts the decisions made by the Star Chamber. Part of the point is that that infrastructure can operate in the sincere belief that its published principles are being upheld.
In conventional imagination, membership of a Star Chamber is achieved only through invitation. If a place becomes available (e.g. through death), or if specific expertise or energy is newly required, then the existing Star Chamber members can identify, and agree to include, a chosen individual.
In turn, that leads to the idea of conspiracies-within-conspiracies. Just possibly, by carefully influencing membership a small number of Star Chamber members might conspire to subvert and control the policies and mission of the Star Chamber itself.
If I am on the mark, you are probably thinking of the 1983 film The Star Chamber, directed by Peter Hyams and starring Michael Douglas. Douglas plays a frustrated young lawyer who wants to take a short cut to simply punishing influential wrongdoers, rather than constantly seeing them go free through a legal system that they routinely manipulate.
The expression 'Star Chamber' itself is certainly much older. Wikipedia suggests several possible origins in English government, perhaps going back as far as Old English, and definitely figuring in later expedient decision-making in Westminster. A summary offered by the National Archive outlines that history, formally starting in the 15th Century.