If a widow and a married man accept each other as husband and wife verbally and they don't disclose this relation in front of any one else is their meeting a sin or not?

Accept each other? Marriage is essential. Islam allows marriage and it must be done in front of priest, it could be small personal event. Just accepting each other as spouses without marriage will be consider sin, zina. And yes a married man can get married to another person with consent of his wife.

Where does the OP ask about Islam?

It's a common question for both Muslims, and Hindis, and the consent of the wife is the key, if indeed its allowed. The OP was not that specific.