In 1633, shortly after his marriage, he gave his Irish lands to his younger brother, Claud, and resigned his title to the King, to be given to Claud; it was recreated on 14 August 1634 (with the precedence of 1617).
Thereafter he was outlawed, attainted and deprived of his Irish peerage and estates; but not the Scottish ones.
However, he died in a naval encounter on his way back to France a few months later, in August 1691, and his brother and heir Charles Hamilton, 5th Earl of Abercorn was able to get the attainder reversed, on 24 May 1692.
James Hamilton, second Marquess of Abercorn was Lord Lieutenant of Ireland in 1868, when he was created Duke of Abercorn, and Marquess of Hamilton of Strabane; both again in the Peerage of Ireland.
Officially, these were not creations but promotions of his existing Irish titles; this matters because the Act of Union 1800 limited the number of Irish creations after the Union.