command -v vim
shows you how the shell currently handles the command vim.
In your case it is not an alias. It may be a shell function or it has been located at /usr/local/bin/vim earlier but you deleted the file or symlink.
If vim is somewhere else in your $PATH then you must make your shell realize the new location:
hash -d vim
If vim is not in your path then you have to either copy / move or link it there (and run hash -d vim if it is a different location) or create an alias, a shell function or a hash entry for it:
alias vim="/foo/bar/vim"
vim () { /foo/bar/vim ; }
hash -p /foo/bar/vim vim