A person who practices or advocates admonishing as a method of instruction or correction.
Admonition + -ist (suffix for someone who practices a doctrine or method). The -ist suffix typically implies a more committed or systematic approach than simple -er.
An admonitionist would be someone who believes in admonishing as a philosophy or method—essentially a 'professional warner'—but like admonitioner, this word is so rare that most dictionaries don't include it.
Complete word intelligence in one call. Free tier — 50 lookups/day.