Establishing a 1 to 1 relationship between tables
I guess that you mean: "every Nurse is an Employee". 

This can be done with (keeping the Employee table as it is):

CREATE TABLE [dbo].[Employee](
    [Id] [int] IDENTITY(1,1) NOT NULL,        -- why not name this EmployeeId ?
    [Name] [nvarchar](100) NOT NULL,
    [StaffNumber] [nvarchar](50) NOT NULL,
    [Salary] [money] NOT NULL,
    [Address] [nvarchar](max) NOT NULL,
    [GenderId] [int] NOT NULL,
    [ContactNumber] [nvarchar](20) NOT NULL,
  CONSTRAINT [PK_Employee] PRIMARY KEY CLUSTERED 
    ( [Id] )
 ) ;


and changing the Nurse table so the primary key is not an IDENTITY and it has a foreign key that references the Employee (Id):

CREATE TABLE [dbo].[Nurse](
    [EmployeeId] [int] NOT NULL,                 -- not IDENTITY !
    [WardId] [int] NOT NULL,
  CONSTRAINT [PK_Nurse] PRIMARY KEY CLUSTERED 
    ( EmployeeId ),
  CONSTRAINT [FK_Employee_Nurse] FOREIGN KEY  
    ( EmployeeId )
    REFERENCES dbo.Employee ( Id )
) ;