Postgresql query to select most recent coming date time

You can use ROW_NUMBER and an INNER JOIN

WITH CTE As (SELECT 
      "subject_id"
      , "date"
      , "start_time"
      , ROW_NUMBER() OVER(PARTITION BY "subject_id" ORDER BY  "date", "start_time") rn
FROM slot_master 
WHERE DATE("date") + "start_time"::time  > DATE('2022-07-3') + '05:00'::time)
SELECT       CTE."subject_id"
,subject_name
      , "date"
      , "start_time" FROM CTE  INNER JOIN  subject_master ON cTE.subject_id = subject_master.subject_id
WHERE subject_master.status = 'active' AND rn = 1

subject_id    | subject_name | date       | start_time
:------------ | :----------- | :--------- | :---------
UHGAwlfrGDFwU | Maths        | 02-08-2022 | 06:00     
X3Sv7nE5HqhXg | Physics      | 01-08-2022 | 09:00     
Y7fHY4mEJmHaS | Chemistry    | 02-08-2022 | 06:00     

db<>fiddle here

In PostgreSQL, you can use select distinct on to accomplish this. So long as the date is of type date and start_time is of type time, this will work:

select distinct on (s.subject_id) s.subject_id, s.subject_name, slot.date, slot.start_time
  from subject_master s
       join slot_master slot
         on slot.subject_id = s.subject_id
 where slot.date + slot.start_time >= '2022-07-30 05:00'
 order by s.subject_id, slot.date, slot.start_time;