You usually do not need to mention a previous unsuccessful application in the cover letter unless it is directly relevant to the story you are telling now.

The current application should focus on why you are a stronger candidate today: new experience, stronger achievements, clearer motivation, or a better fit with the role.

If the prior process created a meaningful relationship with the firm, you can reference that interaction positively without centering the rejection itself.

Use the limited cover-letter space on current evidence. Be prepared to discuss the prior application if asked, but do not make the reapplication sound like an explanation for past failure. The stronger reapplication story is about what you can offer now, not why the previous process did not work out.