Unique identifier field with a conditional
You could use a key table to store the incrementing part of your second ID column.  This solution does not rely on any client-side code, and is automatically multi-year aware; when the @DateAdded parameter passes in a previously unused year, it will automatically begin using a new set of values for the ID2 column, based on that year.  If the proc is consequently used to insert rows from prior years, those rows will be inserted with "correct" values for the increment.  The GetNextID() proc is geared to handle possible deadlocks gracefully, only passing an error to the caller if 5 sequential deadlocks occur when trying to update the tblIDs table.  

Create a table to store one row per year containing the currently-used ID value, along with a stored procedure to return the new value to use:

CREATE TABLE [dbo].[tblIDs]
(
    IDName nvarchar(255) NOT NULL,
    LastID int NULL,
    CONSTRAINT [PK_tblIDs] PRIMARY KEY CLUSTERED 
    (
        [IDName] ASC
    ) WITH 
    (
        PAD_INDEX = OFF
        , STATISTICS_NORECOMPUTE = OFF
        , IGNORE_DUP_KEY = OFF
        , ALLOW_ROW_LOCKS = ON
        , ALLOW_PAGE_LOCKS = ON
        , FILLFACTOR = 100
    ) 
);
GO

CREATE PROCEDURE [dbo].[GetNextID](
    @IDName nvarchar(255)
)
AS
BEGIN
    /*
        Description:    Increments and returns the LastID value from
                        tblIDs for a given IDName
        Author:         Max Vernon / Mike Defehr
        Date:           2012-07-19

    */
    SET NOCOUNT ON;

    DECLARE @Retry int;
    DECLARE @EN int, @ES int, @ET int;
    SET @Retry = 5;
    DECLARE @NewID int;
    WHILE @Retry &gt; 0
    BEGIN
        SET @NewID = NULL;
        BEGIN TRY
            UPDATE dbo.tblIDs 
            SET @NewID = LastID = LastID + 1 
            WHERE IDName = @IDName;

            IF @NewID IS NULL
            BEGIN
                SET @NewID = 1;
                INSERT INTO tblIDs (IDName, LastID) 
                VALUES (@IDName, @NewID);
            END
            SET @Retry = -2; /* no need to retry since the 
                                  operation completed */
        END TRY
        BEGIN CATCH
            IF (ERROR_NUMBER() = 1205) /* DEADLOCK */
                SET @Retry = @Retry - 1;
            ELSE
                BEGIN
                SET @Retry = -1;
                SET @EN = ERROR_NUMBER();
                SET @ES = ERROR_SEVERITY();
                SET @ET = ERROR_STATE()
                RAISERROR (@EN,@ES,@ET);
                END
        END CATCH
    END
    IF @Retry = 0 /* must have deadlock'd 5 times. */
    BEGIN
        SET @EN = 1205;
        SET @ES = 13;
        SET @ET = 1
        RAISERROR (@EN,@ES,@ET);
    END
    ELSE
        SELECT @NewID AS NewID;
END
GO


Your table, along with a proc to insert rows into it:

CREATE TABLE dbo.Cond
(
    CondID INT NOT NULL
        CONSTRAINT PK_Cond
        PRIMARY KEY CLUSTERED
        IDENTITY(1,1)
    , CondID2 VARCHAR(30) NOT NULL
    , Date_Added DATE NOT NULL
);

GO
CREATE PROCEDURE dbo.InsertCond
(
    @DateAdded DATE
)
AS
BEGIN
    DECLARE @NextID INT;
    DECLARE @Year INT;
    DECLARE @IDName NVARCHAR(255);
    SET @Year = DATEPART(YEAR, @DateAdded);
    DECLARE @Res TABLE
    (
        NextID INT NOT NULL
    );
    SET @IDName = 'Cond_' + CONVERT(VARCHAR(30), @Year, 0);
    INSERT INTO @Res (NextID)
    EXEC dbo.GetNextID @IDName;

    INSERT INTO dbo.Cond (CondID2, Date_Added)
    SELECT CONVERT(VARCHAR(30), NextID) + '/' + 
        SUBSTRING(CONVERT(VARCHAR(30), @Year), 3, 2), @DateAdded
    FROM @Res;
END
GO


Insert some sample data:

EXEC dbo.InsertCond @DateAdded = '2015-12-30';
EXEC dbo.InsertCond @DateAdded = '2015-12-31';
EXEC dbo.InsertCond @DateAdded = '2016-01-01';
EXEC dbo.InsertCond @DateAdded = '2016-01-02';


Show both tables:

SELECT *
FROM dbo.Cond;

SELECT *
FROM dbo.tblIDs;


Results:



The key table and stored proc come from this question.