I'm trying to get the Head Paladin to become the Elder... and I'm stuck. What do you do to find an instance where Elder McNamera broke "The Chain that Binds" ?

Go find the 3 holo tapes report back to the elder and then go to hardin with the info. After that you wont be able to do talk to them for awhile so i would recomend continueing the main questline for a bit.

I'd guess you go find the three mission discs that the elder wants but give them to Haldin instead, but i hav'nt completed the quest yet so that might not be it.