A person who works with or handles clay, such as a potter, brickmaker, or clay processor.
From 'clay' plus the agent suffix '-er' (one who does the action), following the standard English pattern for occupational names.
Like 'baker,' 'miller,' and 'tanner,' 'clayer' was a common occupational surname in medieval England, and many people with clay-related surnames descend from ancestors in that trade.
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