The health board said enhanced contact tracing has been carried out.
Close contacts will be asked to isolate for ten days, irrespective of their vaccination status and PCR test result.
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There are three Omicron cases in the NHS Highland area out of 48 across Scotland, according to latest Scottish Government figures published on Sunday.
NHS Highland said: “Until more is known about it we need to be cautious and do everything we can to prevent spread.
“As such, the current isolation advice does not apply and close contacts will be asked to isolate for ten days irrespective of their vaccination status and PCR test result.
“Their households will also be asked to take additional action in order to try to reduce transmission within our communities.
“We are working very closely with the staff at the Royal British Legion who have been supporting the outbreak investigation.”
NHS Highland urged anyone who attended the event and has not yet been contacted by its Health Protection Team or contact tracing team to self-isolate immediately and contact the team on 01463 704886.
A post on the Royal British Legion Nairn Facebook page on December 3 said there was a short-term closure of the venue.
It stated: “Due to a Covid related incident the Nairn Legion is closed for a deep clean. Re-opening, Tuesday 7th December 2021.”