The Eiger Sanction (1975)

Dr. Jonathan Hemlock (Clint Eastwood) is an art history professor and collector who finances his hobby by performing the odd sanction (assassination) for an obscure government bureau. He is forced to take a case where he must find out which of the members of a mountain climbing team is the Russian killer he has been given as a target by joining an expedition to climb the treacherous Eiger.