Lord Dodds of Duncairn, who has been at the heart of the DUP for four decades, has been deputy leader for 13 years.
He was elevated to the Lords after losing his North Belfast seat at Westminster in 2019.
Party leader Arlene Foster has already said she will be stepping down from that role on May 28.
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On Tuesday evening, Lord Dodds said: “Following my appointment to the House of Lords I decided that I would be stepping back from my party role whenever the next internal election cycle occurred.
“Since, under the party rules, Peers are not even part of the party’s electoral college for leadership positions, it would be incongruous and inappropriate to do otherwise.”
However, Lord Dodds added: “I will continue to use my position in Parliament to advance the cause of the Union and to articulate the views of unionists on the future direction of the United Kingdom and on issues affecting Northern Ireland more generally.”