I have a ready First Mate in base, and I use Relentless Pursuit to move it to an open battlefield. Because of Relentless Pursuit, it has "when I conquer, you may move me to base". Will it return to base readied?

Yes, your First Mate will return to your base ready.

According to RiftJudge FAQ #9111 and RiftJudge FAQ #3150, move effects (such as the one granted by Relentless Pursuit) do not change the orientation of a unit unless the card explicitly states that it does (e.g., "move it to your base exhausted"). Since Relentless Pursuit does not specify that the unit must be exhausted or that it enters exhausted, the unit retains its current state.

Sequence of Events:

  1. Movement: You use Relentless Pursuit to move your ready First Mate to a battlefield. It arrives at the battlefield ready.
  2. Conquest: Your First Mate conquers the battlefield.
  3. Trigger: The "When I conquer, you may move me to my base" ability granted by Relentless Pursuit triggers.
  4. Resolution: You choose to resolve the ability and move the unit to your base. Because this is a move effect and not a "Standard Move" (which requires exhausting as a cost), the First Mate arrives at your base in its current state: ready.