The word "suddenly" is already an adverb, meaning it describes a verb, adjective, or another adverb. It is not a phrase.
Adverb phrases are groups of words that function as adverbs. They usually include an adverb and other words that modify it.
Here are some examples of adverb phrases:
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very quickly
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all of a sudden
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in a hurry
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with great care
These phrases describe how, when, where, or to what extent an action is performed.
While "suddenly" can be part of an adverb phrase, such as "all of a sudden," it is not an adverb phrase itself.