Hello, LChi—and welcome to English Forums. Thank you for registering as a member. ) There is no need for present perfect in that sentence.
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LChiI have had a kitten once but he died.(What I meant: The speaker did own a kitten in one point of his life but unfortunately, the kitten died.)There is no need for present perfect in that sentence. We presume that it was preceded by the question, "Have you ever had a kitten?"