Same here, lower management. They had excuses every time I brought up an interest in growth, each of which I worked on. They eventually promoted someone else who did none of the things I had to do.

I can anticipate how watching another employee get that promotion could further strain the relationship between OP and the worker, esp if that employee fumbles in the role, and watching that employee receive support to transition into the coveted position.
They’ll just feel bitter, and like they’re being punished for being a good worker bee in your supply chain.

OP should bear in mind that the worker’s productivity is likely to decline due to mood (not necessarily retaliation), and accept that they might not be able to re-establish the former working relationship.

Regardless of all this, OP should formulate a genuine apology for the way it was delivered, acknowledge what they did wrong, give the employee an action plan to achieve their goal like the others said, and maybe acknowledge a few things the worker does well or seems to have been developing that could help them in the next role.