Testa
SELECT id, crp, starts_on
FROM tbl_crps
NATURAL JOIN (SELECT crp, MAX(id) id
FROM tbl_crps
WHERE starts_on < CURRENT_DATE
GROUP BY crp) x
UNION ALL
SELECT id, crp, starts_on
FROM tbl_crps
NATURAL JOIN (SELECT crp, MAX(id) id
FROM tbl_crps
GROUP BY crp
HAVING MIN(starts_on) >= CURRENT_DATE) x;