Inquisitive American leaving rare object (5)
I believe the answer is:
curio
'rare object' is the definition.
(I've seen this before)
'inquisitive american leaving' is the wordplay.
'inquisitive' becomes 'curious' ('curious' can be similar in meaning to 'inquisitive').
'american' becomes 'us'.
'leaving' indicates named letters should be taken away.
'curious' with 'us' taken away is 'CURIO'.
(Other definitions for curio that I've seen before include "Rare or unusual thing" , "Item of bric-a-brac" , "Odd, unusual object" , "something odd" , "Intriguing object worth collecting" .)