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glossophobia

n. The fear of public speaking.

Wikipedia
Glossophobia

Glossophobia or speech anxiety is the fear of public speaking or of speaking in general. The word glossophobia comes from the Greek γλῶσσα glōssa, meaning tongue, and φόβος phobos, fear or dread. Many people only have this fear, while others may also have social phobia or social anxiety disorder.

Stage fright may be a symptom of glossophobia.