[This is an annotated list of all appearances and all mentions of the gentleman.]
Norman Woodland as Horatio, 1948 [dressed as a gentleman]
"She is importunate, indeed distract: / Her mood will needs be pitied" (4.5.2-3), says the gentleman to the Queen, about mad Ophelia. He goes to fetch Ophelia and doesn't reappear in the scene. [Scene Summary]
"Sea-faring men, sir: they say they have letters for you" (4.6.2), the gentleman tells Horatio when Horatio asks who wants to see him. We don't know if this is the same gentleman who appeared in the preceding scene, and who cares? [Scene Summary]