Taken from the man page:
-n, --no-clobber do not overwrite an existing file (overrides a previous -i option)
Example:
cp -n myoldfile.txt mycopiedfile.txt
Consider using rsync.
rsync
rsync -a -v --ignore-existing src dst
As per comments rsync -a -v src dst is not correct because it will update existing files.
rsync -a -v src dst
cp -n
Is what you want. See the man page.