Inserting ID and Date to locate data for C#/VBA application
-Please don't use short, cryptic column names.
-There's no reason to wrap individual statements in explicit transactions.

You'll want to extract the key value from the table variable in a separate statement.  Something like:

Create Procedure dbo.Insert_Student  
(  
SName varchar(10),  
SAge int,  
SAdmit_Dt date  
)  
BEGIN
    Declare @ids table(id int)
    Declare @pk int 

    BEGIN TRY  

      BEGIN TRANSACTION  

      Insert into dbo.Student(Name,Age,AdmissionDt)  
      OUTPUT INSERTED.S_ID into @id    
      Values  (@SName,@SAge,@SAdmit_Dt);

      set @pk = (Select id from @id);

      Insert into dbo.DB_TRACK (TBL_N, ID, ENTR_DT ) 
      VALUES ('dbo.Student', @pk,GETDATE());

      COMMIT TRANSACTION  

    END TRY  
    BEGIN CATCH

      IF @@TRANCOUNT &gt; 0  
          ROLLBACK TRANSACTION  

      THROW;

    END CATCH
END