MySQL 8.0

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

CREATE TABLE Table1 (
  `CURR_STRT_DT` DATETIME,
  `CUUR_END_DT` DATETIME,
  `product` VARCHAR(1)
);

INSERT INTO Table1
  (`CURR_STRT_DT`, `CUUR_END_DT`, `product`)
VALUES
  ('2019/06/30', '2019/9/28', 'A'),
  ('2019/06/30', '2019/9/28', 'A'),
  ('2019/09/29', '2019/12/28', 'B'),
  ('2019/12/29', '2020/3/28', 'C'),
  ('2019/3/31', '2019/6/29', 'D');
WITH cte as (
    SELECT *,  dense_rank() over (ORDER BY CURR_STRT_DT) as rn
    FROM Table1
)    
SELECT *
FROM cte


CURR_STRT_DT
CUUR_END_DT
product
rn


2019-03-31 00:00:00
2019-06-29 00:00:00
D
1

2019-06-30 00:00:00
2019-09-28 00:00:00
A
2

2019-06-30 00:00:00
2019-09-28 00:00:00
A
2

2019-09-29 00:00:00
2019-12-28 00:00:00
B
3

2019-12-29 00:00:00
2020-03-28 00:00:00
C
4


WITH cte as (
    SELECT *,  dense_rank() over (ORDER BY CURR_STRT_DT) as rn
    FROM Table1
)    
SELECT c1.*, 
       (select `CURR_STRT_DT` FROM cte as c2 WHERE c2.rn - 1  = c1.rn   LIMIT 1) as `CURR_STRT_DT`,
       (select `CUUR_END_DT` FROM cte as c2 WHERE c2.rn - 1= c1.rn LIMIT 1) as `CUUR_END_DT`
FROM cte c1;


CURR_STRT_DT
CUUR_END_DT
product
rn
CURR_STRT_DT
CUUR_END_DT


2019-03-31 00:00:00
2019-06-29 00:00:00
D
1
2019-06-30 00:00:00
2019-09-28 00:00:00

2019-06-30 00:00:00
2019-09-28 00:00:00
A
2
2019-09-29 00:00:00
2019-12-28 00:00:00

2019-06-30 00:00:00
2019-09-28 00:00:00
A
2
2019-09-29 00:00:00
2019-12-28 00:00:00

2019-09-29 00:00:00
2019-12-28 00:00:00
B
3
2019-12-29 00:00:00
2020-03-28 00:00:00

2019-12-29 00:00:00
2020-03-28 00:00:00
C
4
null
null

CURR_STRT_DT	CUUR_END_DT	product	rn
2019-03-31 00:00:00	2019-06-29 00:00:00	D	1
2019-06-30 00:00:00	2019-09-28 00:00:00	A	2
2019-06-30 00:00:00	2019-09-28 00:00:00	A	2
2019-09-29 00:00:00	2019-12-28 00:00:00	B	3
2019-12-29 00:00:00	2020-03-28 00:00:00	C	4