Here's your original sentence:
Is it time the institutions peddling fashion's next generation followed suit to address what's not working?
First, take a look at this sentence:
I say it's time we got the hell of here! Or else we're gonna get killed by that angry mob!
The pattern that's used in this example is as follows:
It is time I/you/we did something.
This type of phrasing is employed when you want to say that it would be a rather good or very reasonable idea to do something.
So, here's my interpretation of your sentence:
Is it time that the institutions (organizations that sell clothes, clothing manufacturers etc.) that are peddling fashion's next generation (promoting the next generation of fashionable clothes) followed suit (did the same thing as, I presume, companies, firms etc. in other industries are doing) to address what's not working (it would be a good idea if they started asking questing about what is wrong with this new generation of things to wear)?
Without the parenthetical stuff:
Is it time that the institutions that are peddling fashion's next generation followed suit to address what's not working?
Is it time that the institutions...
The institutions that are peddling fashion's next generation.
Is it time that they did what?
It is time that they followed suit.
For what reason?
To address what is not working.