Assign row numbers in partitions of AgreementNo, ElementStartDate, DateSeqNo
and update those rows where the row number is greater than 1:
WITH ranked AS (
SELECT
ElementStartDate,
rn = ROW_NUMBER() OVER (PARTITION BY AgreementNo, ElementStartDate, DateSeqNo
ORDER BY (SELECT 1)) -- actual order probably
-- doesn't matter here
FROM WASP_Mart_EmbassyActuarial.dbo.tblARM_OmegaSource
)
UPDATE ranked
SET ElementStartDate = ElementStartDate + rn - 1
WHERE rn > 1
;
This method can handle cases with more than two duplicates in a group, although, of course, with very many duplicates it may start producing new ones instead.