Tell him not _ anyone enter the enclosure:

Explanation

The correct answer is 'Let.' The sentence structure 'Tell him not let anyone enter the enclosure' is a command or directive. In English, after verbs like 'tell,' we use the base form of the verb without 'to' for commands, making 'let' the correct choice. 'To let' is incorrect as it improperly introduces a to-infinitive. 'To have let' suggests a completed action, which does not match the present intent. 'Telling' is a present participle, not suitable for the imperative sentence structure.