HMS Annan was a River-class frigate built for the Royal Navy but was transferred to the Royal Canadian Navy before commissioning. She served with the Royal Canadian Navy during the Second World War and saw action primarily as a convoy escort in the Battle of the Atlantic. She was returned to United Kingdom and quickly sold to Denmark, who renamed her Niels Ebbesen. She was primarily used as a training vessel until 1963 when she was broken up in Odense. She was named for the River Annan in Scotland.