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This reminds me of the trope I've seen where a gym teacher or sports coach acts like a military drill instructor, as seen with Coach Buzzcut from Beavis and Butt-Head and Coach Oleander from Psychonauts.
Wrong Line of Work seems related but that seems more like it's for a character who is unsuited for their line of work, whereas you're asking for a character who dresses and acts like a professional from a different line of work but is still effective in their current job.
EDIT: A closer look at Wrong Line of Work seems like the first two paragraphs indeed describe what you're looking for. It says sometimes the character in question is suited to their current job, but has a "mindset that would be better suited for some other position."
Edited by FerrousFaucetSeconding Wrong Line of Work, but the cases where they're good at the job can overlap with Bunny-Ears Lawyer.

A character's characterization and behavior is at odds with their current job, though they're usually good at said job.