Legal small claims imput for apartment rental wanted. Question about lease.?

Once the contract is over/new tenant found/in place and paying rent

if the small claims in your state allows 6 yrs to claim in small claims, the time will start when the eviction notice was official by a court decision

The landlord can sue for unpaid rent the day it's late. That's probably when the statute of limitation on THAT claim starts. If the tenant left damages when vacating, then the date of their departure would be a good place to start the clock on THAT part of the claim. If it's a claim by the tenant for refund of the security deposit, that wouldn't start until 21 days after departure, depending upon how the lease was terminated. Of course, the landlord may only claim compensation for unpaid rent if he or she can prove "reasonable efforts" to mitigate their losses. Ref. WI Statutes 704.29.

It starts when the offense occurs.

The person pays for the lease until it is re rented. The rent stops on the day the new tenant pays the rent. You are only held for that amount and nothing more. They can not charge for double rents.

The clock starts the day after the tenant vacates the apartment.

What's your claim for? What money?