How are your history rows ordered in the table? In other words, how do you decide which history rows to compare to see if a value was changed? And how do you uniquely identify a history row entry?
If you order your history rows by start_dt, for example, you can compare the previous and current row values using window functions, like Rob suggested:
UPDATE MyHistoryTable
FROM (
-- Get source history rows that need to be updated
SELECT
history_row_id, -- Change this field to match your table
MAX(status_cd) OVER(ORDER BY start_dt ROWS BETWEEN 1 FOLLOWING AND 1 FOLLOWING) AS status_cd_next, -- Get "status_cd" value for "next" history row
MAX(phase_cd) OVER(ORDER BY start_dt ROWS BETWEEN 1 FOLLOWING AND 1 FOLLOWING) AS phase_cd_next,
MAX(start_dt) OVER(ORDER BY start_dt ROWS BETWEEN 1 FOLLOWING AND 1 FOLLOWING) AS start_dt_next
FROM MyHistoryTable
WHERE status_cd <> status_cd_next -- Check "status_cd" values are different
OR phase_cd <> phase_cd_next -- Check "phase_cd" values are different
) src
SET MyHistoryTable.end_dt = src.start_dt_next -- Update "end_dt" value of current history row to be "start_dt" value of next history row
WHERE MyHistoryTable.history_row_id = src.history_row_id -- Match source rows to target rows
This assumes you have a column to uniquely identify each history row, called "history_row_id". Give it a try and let me know.
I don't have a TD system to test on, so you may need to futz with the table aliases too. You'll also probably need to handle the edge cases (i.e. first/last rows in the table).