of consequence
Important; significant; having value. We only have a limited amount of time in which to conduct this meeting, so let's please stick to matters of consequence. He was the only person of consequence at the party, so once he left, I felt there was no longer a reason to stay.
of consequence
Important, as in For all matters of consequence we have to consult the board, or Only scientists of consequence have been invited to speak. This idiom was first recorded in 1489.