Are you able to disassemble everything, especially are you able to separate the membrane from the rest of the reference electrode? If so, you can clean the membrane with any oxidizing agent (acidic, I guess that HNO3 should work) and wash it thouroughly with acetone, ethanol and destilled water without risking to contaminate or change the Ag/Ag+ electrode itself. I would in any case replace the electrolyte (KCl-solution probably) in contact with the Ag/AgCl.
If you are unable to separate the parts of the electrode, then you have to prepare a new Ag/AgCl electrode contact. But there are ways describe in the internet, see