With the Tunnel Master fighting style (from Unearthed Arcana: Light, Dark, Underdark!), a character can use a bonus action to take a defensive stance that lets them make opportunity attacks without expending a reaction.
The Oath of Vengeance paladin gets the Relentless Avenger feature at 7th level (PHB, p. 88); when he makes an opportunity attack, he can move up to half his speed as a part of the reaction used to make the attack.
Can a character in a Defensive Stance with Relentless Avenger move with every opportunity attack? Can he move only once, expending his reaction, while still having unlimited opportunity attacks otherwise?
Best Answer
As you stated, Relentless Avenger allows you to move your speed as part of the reaction used on the Opportunity Attack. You are not expending a reaction when you use Tunnel Master's defensive stance to make opportunity attacks, thus you cannot move.
Can a character in a Defensive Stance with Relentless Avenger move with every opportunity attack?
No, because he is not using his reaction to make those opportunity attacks, and Relentless Avenger requires it.
Can he move only once, expending his reaction, while still having unlimited opportunity attacks otherwise?
I would say maybe, but you should ask your DM. In the spirit of Tunnel Master, probably not, because in my mind, a defensive stance means you aren't moving.