Oracle 18c

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

WITH tmp AS
    (
        SELECT 12345 AS id, 	TO_DATE('07-Aug-15', 'DD/MON/YY') AS Start_date, 	TO_DATE('07-Aug-65', 'DD/MON/YY') AS End_date FROM dual UNION ALL
        SELECT 12345 AS id, 	TO_DATE('22-Aug-15', 'DD/MON/YY') AS Start_date, 	TO_DATE('01-Jan-16', 'DD/MON/YY') AS End_date FROM dual UNION ALL
        SELECT 12345 AS id, 	TO_DATE('24-Mar-16', 'DD/MON/YY') AS Start_date, 	TO_DATE('23-Mar-66', 'DD/MON/YY') AS End_date FROM dual UNION ALL
        SELECT 12345 AS id, 	TO_DATE('06-Jul-16', 'DD/MON/YY') AS Start_date, 	TO_DATE('31-Dec-17', 'DD/MON/YY') AS End_date FROM dual UNION ALL
        SELECT 12345 AS id, 	TO_DATE('31-Dec-16', 'DD/MON/YY') AS Start_date, 	TO_DATE('31-Dec-41', 'DD/MON/YY') AS End_date FROM dual UNION ALL
        
        SELECT 4662828 AS id, 	TO_DATE('22-Aug-15', 'DD/MON/YY') AS Start_date, 	TO_DATE('22-Dec-15', 'DD/MON/YY') AS End_date FROM dual UNION ALL
        SELECT 4662828 AS id, 	TO_DATE('01-Jan-16', 'DD/MON/YY') AS Start_date, 	TO_DATE('01-Aug-18', 'DD/MON/YY') AS End_date FROM dual UNION ALL
        SELECT 4662828 AS id, 	TO_DATE('10-Jun-17', 'DD/MON/YY') AS Start_date, 	TO_DATE('31-Dec-18', 'DD/MON/YY') AS End_date FROM dual UNION ALL
        SELECT 4662828 AS id, 	TO_DATE('01-Dec-18', 'DD/MON/YY') AS Start_date, 	TO_DATE('04-Dec-72', 'DD/MON/YY') AS End_date FROM dual 
    )
    , tmp1 AS
    (
        SELECT 
            CONNECT_BY_ROOT t.start_date AS start_date,
            t.id,
            t.start_date AS start_date1,
            t.end_date,
            level AS lvl
        FROM tmp t
        CONNECT BY PRIOR id = id AND PRIOR start_date <> start_date AND PRIOR end_date <> end_date 
            AND PRIOR end_date BETWEEN start_date AND end_date
    )
    , tmp2 AS 
    (
        SELECT *
        FROM tmp1
        WHERE (start_date, id, lvl) IN
            (
                SELECT start_date, id, MAX(lvl)
                FROM tmp1
                GROUP BY start_date, id
            )
    )
    SELECT id,
        MIN(start_date) AS start_date,
        end_date
    FROM tmp2
    GROUP BY id, end_date
    ORDER BY id, start_date;

ID	START_DATE	END_DATE
12345	07-AUG-15	23-MAR-66
4662828	22-AUG-15	22-DEC-15
4662828	01-JAN-16	04-DEC-72