Learn Dutch: Je hoeft de gijzelaar nog niet vrij te laten. - You do not have to release the hostage yet.

Vrijlaten (to set free) is a separable verb. When a separable verb is used as a te infinitive, the word te is squeezed between the separable prefix (vrij) and the root verb (laten), written as three separate words: vrij te laten.

Does hoeft ... niet mean 'must not'?

No, hoeven combined with a negative like niet means 'do not have to' or 'do not need to'. If you wanted to strictly forbid the action and say 'You must not release the hostage', you would use mogen instead: Je mag de gijzelaar niet vrijlaten.

Is de gijzelaar the semantic subject of the te infinitive here, as it would be with a verb like dwingen?

No, this is a bit different from verbs like dwingen (to force) where the object does the action. Here, hoeven acts like a modal verb for the main subject Je. You are the one doing the releasing, and de gijzelaar is simply the direct object receiving the action of vrij te laten.

Why does nog niet come before the infinitive clause?