removal of trace carbonate from alkaline electrolyte is very tricky. When I work with alkaline solutions of high purity, I usually end the experiment when I see telltale signs of carbonate.
What you would like to try first of all is start with ultra-high-purity alkaline electrolyte, keeping it de-aerated to avoid CO2 from the air to dissolve in the electrolyte. When I work with these chemicals in this way I can usually keep carbonate out for a few hours.
The removal of carbonates from NaOH solution is usually done by concentrating the NaOH to 50 wt-%, then waiting for the less soluble Na2CO3 to precipitate, which is very time consuming. A quick literature seach shows me that a group recently claimed to have an other method, which requires 8M NaOH, with added CaO and stirred overnight. But this in either case is not in-situ removal!
better to start without carbonates, and trying to keep them out.