Learn Finnish: Valtuustossa järjestettäneen uusi keskustelu kompromissia varten. - A new discussion will probably be organized in the council for the compromise.

It comes from the verb järjestää (to organize). You take the passive stem järjestettä- (which you can see in the standard present passive järjestetään), add the potential marker -ne-, and finish with the passive ending -en. The potential mood adds the meaning of "probably" or "likely" to the passive action.

The potential mood here is in the present tense, but the English translation says "will probably be". Why is that?

The Finnish present potential can refer to either a present probability ("is probably being organized right now") or a future probability ("will probably be organized"). Context determines the time frame. Here, organizing a new discussion naturally implies a future event.

Why is "uusi keskustelu" in the basic nominative case here instead of the genitive-accusative object case?

In Finnish, when a sentence is in the passive voice, a total object takes the nominative case instead of the genitive-accusative (which would be uuden keskustelun). Because järjestettäneen is a passive verb, the object uusi keskustelu stays in its basic dictionary form.

Why is "kompromissia" in the partitive case?

It is required by the postposition varten (for the purpose of / meant for). The noun immediately preceding varten must always be in the partitive case.