I have the same pump labeled as the Medai "Top" that I've had for over 20 years. Mine still works and I was able to find a replacement chuck insert about 10 years ago but I don't think I could now.
AFAIK, these have been out of production for many years and replacement/rebuild parts are difficult to impossible to find. Loose Screws has every part needed to rebuild any Silca pump but nothing for the Media. Maybe hunting around older bike shops will turn up something but even NOS inserts will be quite old and may not work well.
One way to get more use out of the pump would be to fit a modern replacement chuck to the current air hose.