Вам не нужен триггер или какой-либо код для всего этого. Создайте FK от EMPLOYEE_MANAGER_ID до EMPLOYEE_MANAGER_ID с опцией удалить заданный ноль.
CREATE TABLE "EMPLOYEE_LEAVE"
( "EMPLOYEE_ID" NUMBER NOT NULL ENABLE,
"EMPLOYEE_NAME" VARCHAR2(100) NOT NULL ENABLE,
"EMPLOYEE_EMAIL" VARCHAR2(100) NOT NULL ENABLE,
"EMPLOYEE_MANAGER_ID" NUMBER,
"EMPLOYEE_USERNAME" VARCHAR2(400),
"EMPLOYEE_LEAVE_NORMAL" NUMBER NOT NULL ENABLE,
"EMPLOYEE_LEAVE_LOP" NUMBER,
"EMPLOYEE_IS_MANAGER" CHAR(1) NOT NULL ENABLE,
"EMPLOYEE_IS_ADMIN" CHAR(1) NOT NULL ENABLE,
"EMPLOYEE_CONTACT_NO" VARCHAR2(100),
"EMPLOYEE_PASSWORD" VARCHAR2(100),
CONSTRAINT "EMPLOYEE_PK" PRIMARY KEY ("EMPLOYEE_ID")
USING INDEX ENABLE
, constraint empmgr_2_emp foreign key (employee_manager_id)
references employee_leave(employee_id) on delete set null
);