BRUSSELS—European Union and British negotiators on Monday agreed on the terms of the U.K.’s 21-month transition after it leaves the bloc next March, but left unresolved a thorny issue—the future of Ireland—that could derail the entire Brexit deal.

The new agreement opens the way for talks on the U.K.’s future economic and security relationship with the bloc, something the U.K. has long asked for. But while the transition was relatively easy to agree on, the most difficult phase of negotiations still lies ahead.

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