Can I play Thrill of the Hunt in opponent turn and conquer a battlefield that I am standing on?

Yes, you can. On your opponent's turn, play Thrill of the Hunt (a [Reaction]) to banish a friendly unit and play it to any battlefield you don't control. When it arrives, the battlefield becomes Contested, triggering a Non-Combat Showdown. If you win that showdown — meaning your unit is the only one left — you establish control and Conquer, scoring a point (Rules 344.2, 348.2, 464.1).

A few important limits:

• Once per battlefield per turn. You can only score from that battlefield once (Rule 465). If you already scored it this turn, you won't get a second point.
• Winning Point restriction. If this would be your final point to win (e.g., from 7 to 8 in standard 1v1), you must have scored every other battlefield this same turn to gain the point via Conquer. Otherwise you draw a card instead (Rule 466.1.b.2, FAQ #11423).
• No win on opponent's turn. Even if you hit the victory score, the game only checks for a winner during a cleanup — the turn still belongs to your opponent, so the game won't end until that cleanup occurs (Rule 323.1).