Clark, who took the reins at the League One club last week, worked under the experienced coach during his time as a Magpies player.
McDermott, 57, has been out of work since Kevin Keegan ended his second spell in charge of the Premier League club in September.
"Terry is vital to what we are trying to achieve here. He brings vast experience to the club both from his player and coaching days," Clark told the club's official website.
"He has worked with us all at various stages in our careers - he was assistant manager at Newcastle when I was a player and then a coach.
"Terry is very good at building relationships with the players and getting them bubbly, which is important as there will be times when we need to lift them for one reason or another."