Can you play a land during a extra turn granted by Time Walk effects?

Each turn — whether a normal turn or an extra turn granted by a card like Time Walk, Time Warp, or Temporal Manipulation — proceeds through the full sequence of phases and steps defined in CR 500.1. There is nothing in the rules that distinguishes extra turns as 'partial' turns; they are complete turns in every sense.

The rule governing land plays is CR 305.1, which states that a player may play one land on each of their turns during their main phase (assuming no effect has increased or decreased that number). Because an extra turn is still your turn, you get a fresh land-play allowance for that turn.

Crucially, the land-play count resets each turn (CR 305.3 tracks how many lands have been played 'this turn,' and 'this turn' resets when a new turn begins per CR 500.1). So finishing your normal turn having already played a land does not carry over to the extra turn — you start fresh.

Concrete example: You play a Forest on your normal turn, then cast Time Warp to take an extra turn. When that extra turn begins, your land-play count resets. During your extra turn's main phase, you may play another land — say, a Mountain — completely legally.

The only caveat is that any effect currently limiting or expanding land plays (e.g., Fastbond granting additional land plays, or a Mana Vortex effect) would still apply on the extra turn if it is still in effect, since those modify the number available during any given turn you take.