Simple question really: does REP roll over when you advance from Weak to Strong Hold and from Tier to Tier? What happens when the Crew caps REP and does not have the COIN to advance Tier?
My interpretation of page 44 in the rulebook is that Rep does not rollover. The rep track remains full, with no additional counting, until the crew either moves from weak hold to strong hold or moves up a tier. Then the rep track goes to zero with no roll over.
Therefore, if a crews rep track is full and they have yet to move up a tier, they will not gain anymore rep through new actions.