Implicit conversion from data type datetime to int is not allowed. Use the CONVERT function to run this query.

INSERT INTO newNBOCAP_CARE_PLANS_WITH
SELECT CARE_ID, MAX(EVENT_DATE) AS EVENT_DATE, MAX(EVENT_ID) AS EVENT_ID, Username FROM
(SELECT i.CARE_ID, EVENT_DATE, EVENT_ID, Username FROM newNBOCAP_CARE_PLANS i
JOIN
(SELECT CARE_ID, MIN(EVENT_DATE) FirstTRDate
FROM newNBOCAP_CARE_PLANS
WHERE EVENT_TYPE IN ('BR','CH','TE','SU')
GROUP BY CARE_ID) FirstTP
ON FirstTP.CARE_ID = i.CARE_ID
WHERE
i.EVENT_TYPE = 'CARE_PLAN' AND
i.EVENT_DATE <= FirstTP.FirstTRDate) a
GROUP BY CARE_ID, Username