Stephen Corrigan, 43, whose address was given as Blantyre, made no plea to the charge of attempting to defeat the ends of justice.
He was remanded in custody for a further court appearance in the next eight days.
Last month, Amber’s brother Connor Gibson appeared at the same court charged with murdering and sexually assaulting her as well as attempting to pervert the course of justice.
The 19-year-old made no plea and was remanded in custody pending a further court appearance.
Amber, 16, who attended a specialist education unit in West Lothian, left her home in the Hillhouse area of Hamilton, at about 9.15pm on Friday November 26 and was reported missing later that night.
Her body was discovered in the town’s Cadzow Glen park at about 10.10am the following Sunday.