The participle phrase in the above sentence is 'Enjoying her new flute.'
The participle phrase starts either with the present (dependably ending with -ing) or past (dependably ending with -ed)
The participle phrase includes the modifiers or objects to complete the thought of the sentence. For instance, in the above sentence 'enjoying' is in present and modifies the word 'new flute'. Therefore, the participle phrase acts as an adjective always, providing a description of the sentence,