Answer: gosteady

AnswerCrossword Clue
GOSTEADYDate exclusively
GOSTEADYDate one person exclusively
GOSTEADYDon't see other people, perhaps
GOSTEADYBe part of an exclusive deal?
GOSTEADYBecome an item
GOSTEADYDate, in a way
GOSTEADYHave an exclusive relationship