or possibly
state related liability
Zustand = state, condition

apart from other liabilities, there is a liability which is directly linked to the condition or state of repair of the property, i.e. an old premises in poor condition could prove a higher liability, than a new premises

Translation of sentence: "The lessor shall settle (or adjust) claims deriving from the condition of the premises."
I agree that we are dealing with premises liability her, but I prefer the above translation to: "claims deriving from premises liability."
The latter sounds too German.

Regards, Dr. Thomson, J.D.

Your profile indicates that you are also located "down under" - my answer is based on NZ law which is, in fact, very similar to the principles underlying Australian law.

"Zustandshaftung" follows from section 536 of the German Civil Code (BGB) which requires the lessor/landlord to keep the leased premises in a tenantable condition for the duration of the lease, i.e. to repair the premises.

Except under a lease for residential premises, in accordance with NZ (and presumably Australian) law the lessor/landlord is not generally liable to repair and keep the premises in a tenantable condition unless there is an express covenant to do so. This covenant is commonly referred to as "a covenant to repair" (supported by Romain: "covenant" or "obligation to repair" = "Unterhaltungspflicht, Instandsetzungspflicht").

Now, the fundamental difference being that under German law, "Zustandshaftung" is an implied obligation under the law, but under English/NZ/Australian law this obligation must be established by an express covenant in the commercial lease document (although some English cases suggest that it may also be implied - ok, let's not go there), I would suggest the above translation, as this reflects the underlying legal principle of your sentence.

I could rattle on - please feel free to contact me if you need more information.