Oracle 18c

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
CREATE TABLe staff(StaffNo int, department int,
  CONSTRAINT staff_pk PRIMARY KEY (StaffNo))
INSERT INTO staff VALUES(1,1)
1 rows affected

INSERT INTO staff VALUES(2,2)
1 rows affected

INSERT INTO staff VALUES(3,1)
1 rows affected

INSERT INTO staff VALUES(4,1)
1 rows affected

CREATE TABLE teachers (tID int , ClassteacherNo int , subteacherNo int
  , CONSTRAINT fk_ClassTeacher
    FOREIGN KEY (ClassteacherNo)
    REFERENCES staff(StaffNo)
  , CONSTRAINT fk_SubTeacher
    FOREIGN KEY (subteacherNo)
    REFERENCES staff(StaffNo))
INSERT INTO teachers VALUES(1,1,3)
1 rows affected

CREATE OR REPLACE TRIGGER teachers_before_update
BEFORE UPDATE
   ON teachers
   FOR EACH ROW

DECLARE
   v_teacher_dep int;
   v_subteacher_dep int;
BEGIN

   -- Find department for teacher
   SELECT department INTO v_teacher_dep
   FROM staff 
  WHERE StaffNo = :new.ClassteacherNo;

   -- Find department for subteacher
   SELECT department INTO v_subteacher_dep
   FROM staff 
  WHERE StaffNo = :new.subteacherNo;


    IF v_subteacher_dep <> v_teacher_dep
      THEN
        RAISE_APPLICATION_ERROR(-20002,'The deaprtment differs between teacher and subteacher');
    END IF;
END;

/
SELECT * FROM USER_ERRORS;
UPDATE teachers SET subteacherNo = 2 WHERE tID = 1
ORA-20002: The deaprtment differs between teacher and subteacher
ORA-06512: at "FIDDLE_UUXCZJDQDWCKIGQJJFBH.TEACHERS_BEFORE_UPDATE", line 19
ORA-04088: error during execution of trigger 'FIDDLE_UUXCZJDQDWCKIGQJJFBH.TEACHERS_BEFORE_UPDATE'

UPDATE teachers SET subteacherNo = 4 WHERE tID = 1
1 rows affected