I have a unit on a battlefield on my beginning phase. My battlefield triggers some effect when I hold, can I use Thrill of the Hunt and play the unit on the other empty battlefield and get both points from holding?

To answer your question, we must look at how holding and scoring work in the Beginning Phase.

The Ruling

No, you cannot get two points from holding in this scenario.

According to Rule 465, a player may only score (via either Conquer or Hold) once per battlefield per turn. Moving your unit to a different battlefield does not grant you a second "Hold" point for the turn, nor does it allow you to trigger a Hold effect at a new location after the Beginning Phase has already processed.

Sequence and Reasoning

1. Beginning Phase: Your "Hold" triggers occur during your Beginning Phase when you maintain control of a battlefield and score a point.
2. Thrill of the Hunt Timing: While Thrill of the Hunt is a [Reaction] that can be played at almost any time, playing it after you have already scored your holding point for the turn will not retroactively trigger a new "Hold" event.
3. Hold Definition: Per Rule 383.4.d, Hold effects are triggered by the specific action of maintaining control during the Beginning Phase and scoring. Once that phase has passed or that specific scoring event has occurred, you cannot trigger it again.
4. Score Limitation: Even if you were to move the unit to an empty battlefield, Rule 465 strictly limits you to one score per battlefield per turn. Because you have already scored for the turn, you cannot gain another point from holding.

Summary: You can move your unit to another battlefield using Thrill of the Hunt, but you will not gain a second point from holding, and you cannot trigger a "Hold" effect at the second battlefield because the conditions for a "Hold" (maintaining control during the Beginning Phase) have already been met and processed for the turn.