If your data is like

You can write below sql

SELECT QUARTER_NUM,

  MIN(START_DATE),

  MAX(END_DATE)

FROM <Period_table>

WHERE PERIOD_NAME LIKE '%17'

AND application_id = 200

AND ledger_id      = 2021

GROUP BY QUARTER_NUM

order by QUARTER_NUM;

Alternatively if you want to get start date and end date of current quarter, you can add more where clause  as below

SELECT QUARTER_NUM,

  MIN(START_DATE),

  MAX(END_DATE)

FROM gl_period_statuses gps1

WHERE PERIOD_NAME LIKE '%17'

AND application_id = 200

AND QUARTER_NUM   IN

  (SELECT QUARTER_NUM

  FROM gl_period_statuses gps2

  WHERE sysdate BETWEEN START_DATE AND END_DATE

  AND gps2.application_id =  gps1.application_id

  AND gps2.ledger_id =  gps1.ledger_id

  )

AND ledger_id = 2021

GROUP BY QUARTER_NUM

ORDER BY QUARTER_NUM;

Output will be

or below from second sql