We have a team of 20 people divided in 2 teams and a jira bord for both of them. We work on agile scrum methodology.
The team components are a pm/scrum master, BA, PO, testing team, ux,ui and backend dev team. The problem we have is that the bord gets messy and no one is taking care of it.
My question is who should take care of the bord to not get a mess pm, scrum master dev team?
Ideally it is the Scrum teams responsibility (everybody). The beauty of Agile lies in self driven and empowered teams. Don't try to command and control and make it habit of everyone. "Scrum master/PO" can facilitate this (help other team members to close task/US after discussion of their state see point no 2 below). If you try to hold one person responsible for it you will loose granular info and your Agile/Jira board will not reflect actual info.
"The problem we have is that the board gets messy and no one is taking care of it."
If your team follow agile properly this situation will not occur.
"Re-iterating: you can request PO or scrum master to facilitate/watch it. but better to ask your team member to take this responsibility. or Story owner should make sure his/her user story [JIRA in your case] reach to a conclusive state and cleaned up in JIRA."