Oracle 21c

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alter session set nls_date_format = 'YYYY-MM-DD HH24:MI:SS'
select sysdate as today,
  trunc(sysdate, 'Q') as current_q_start,
  add_months(trunc(sysdate, 'Q'), 3) as next_q_start,
  add_months(trunc(sysdate, 'Q'), 6) as following_q_start
from dual


TODAY
CURRENT_Q_START
NEXT_Q_START
FOLLOWING_Q_START


2024-02-27 09:16:08
2024-01-01 00:00:00
2024-04-01 00:00:00
2024-07-01 00:00:00


select date '2022-07-12' as today,
  trunc(date '2022-07-12', 'Q') as current_q_start,
  add_months(trunc(date '2022-07-12', 'Q'), 3) as next_q_start,
  add_months(trunc(date '2022-07-12', 'Q'), 6) as following_q_start
from dual


TODAY
CURRENT_Q_START
NEXT_Q_START
FOLLOWING_Q_START


2022-07-12 00:00:00
2022-07-01 00:00:00
2022-10-01 00:00:00
2023-01-01 00:00:00