In this particular situation, I cannot decide if the comma before "and should be approved" is needed because it is part of the series before it, or it is a compound predicate situation in which the comma is not needed. I do not have the option to reword the sentence.
The cost for the new service is fair, just, and reasonable, and should be approved by the Board.
Generally, we don't include a comma before the and if we're combining two parts of a single clause. For example, you wouldn't use a comma in a sentence like (a) "I like bread and butter" or (b) "I like bread and dislike butter." Your sentence is like (b) in that you've got a Subject ("the cost for the new service") and a Verb Phrase ("is...") and then you throw in a second Verb Phrase ("should be...").
If you like, you could rephrase the sentence so that you have two full clauses, and then you could have a comma: (c) "The cost for the new service is fair, just, and reasonable, and it should be approved by the board". Unless they're very tiny clauses, like in "I like cats and I love dogs," you generally need a comma before the and when connecting two clauses. Adding it (a subject) makes the part after and a complete clause.
I believe that this is something that most grammar books and style guides would agree on, but I can't be sure. Kolln & Funk ("Understanding English Grammar") explains it this way. I also suspect that you yourself would normally avoid a comma in sentences like (b) and that the thing that's confusing you here is that the "and reasonable and should" part looks weird to you. My friend who is a professional copy editor uses the rules I've shared, and it's what I teach to my students if they ask. (I'm a professor of applied linguistics and have taught a lot of writing courses as well. I also teach a class strictly focused on grammar.)
I'm American and it's always possible that what I say applies only to American English, but I think this applies to British English too.
