It should be no problem to get your Name_
column with joining the DESTINATION_CITY
table:
SELECT
contract.Description,
Destination_City.Name_,
contract_type.type AS 'Contract Type',
contract.Tour_Summary AS 'Tour Name',
employee.First_Name AS 'First Name',
employee.Last_name AS 'Last Name',
Currency_.Currency_Name AS 'Currency',
contract_Items.twin AS 'Twin Rate',
contract_items.Item_Rate AS 'Rate'
FROM
Contract
INNER JOIN Employee
ON Contract.Contracted_By_Employee_Id = Employee.Employee_Id
INNER JOIN Contract_Items
ON Contract.Contract_ID = Contract_Items.Contract_ID
INNER JOIN Currency_
ON Contract.Currency_Id = Currency_.Currency_Id
INNER JOIN Contract_Type
ON Contract.Contract_Type_Id = contract_type.Contract_Type_Id
INNER JOIN Destination_City
ON Destination_City.Destination_City_ID = Contract_Items.Destination_City_ID
Please note that the order of the join operations is irrelevant, if you have inner joins only. It's only required that one of the tables is already joined before.