The sentence is: "She loves to play the piano in her free time." The word in question is "loves." To identify its part of speech, its function within the sentence must be examined.
A verb denotes an action, event, or state. "loves" in this sentence signifies the action performed by the subject, "She." It specifies what the subject is doing.
A noun names a person, place, thing, or idea. An adjective modifies a noun, offering more detail about its attributes. An adverb modifies a verb, adjective, or another adverb, typically indicating how, when, or to what extent.
Given its role in expressing the action of the subject "She," "loves" is a verb. Therefore, the part of speech for "loves" is Verb.