As the Wki said,
Gate Progress
Entrance to a subtown, the first levels of tiers 2 and 3, is only free for that gate if a knight has reached that subtown from the previous tier in a previous run. Clearance for free tier entrance is separate for each gate, so new runs from the top are required as new gates become active. Gate progress is shown on the Progress tab of the Character window; free entry is marked by a filled star, while paid entry is marked by an empty star.
Tier 1 - Depth 0-7; always free entry
Tier 2 - Depth 8-17; paid entry: 200 crowns
Tier 3 - Depth 18-28; paid entry: 500 crowns
so..
The free tier 2 entry need to to gained by playing through Tier 1..but once the gate changes,it need to be gained again,right?
or we have to pay 200 extra crowns for each elevator in Tier 2/3?
It's specific to each gate -
You need to complete tier 1 in a specific gate in order to get free access to tier 2 in that gate, for example.
Also, the tier 3 fee is 500 cr.