Should I polish the paint after using a clay bar?

Not always. Fine clay used correctly on harder paint may leave few visible scratches, while aggressive clay or soft paint can show noticeable haze or very fine scratches. Inspect the surface under good lighting before deciding whether polishing is necessary. If claying is done as preparation for a coating, a polishing step is often planned anyway. If only light haze appears and no coating is planned, a sealant or wax can be applied directly, while visible fine scratches on dark paint usually justifies a finishing polish.

References
  1. Polishing (Glossary of Detailing Terms), International Detailing Association (IDA)
  2. Polishing, Wikipedia
  3. Abrasive, Wikipedia
Detailing Dictionary87 technical terms explained in plain English, from beading to wet sanding. Open the dictionary