Given your current setup
sudo vim "$(v)"
will use command substitution to run your alias
v and insert its output into the command line to be run before executing it, so it would run
sudo vim /usr/bin/dict in the end. The quotes make sure it comes out as a single argument, and
$(...) handles running the command and capturing its output.
This will only work from your interactive shell, since aliases aren't used elsewhere. If you want to access it from a script, you could make a small script somewhere in your
PATH variable with the same command inside it.
You've tagged this bash but then shown an extract from
.zshrc, so note also that zsh has "global aliases" that expand anywhere:
alias -g v='"$(xclip -selection c -o)"'
and then just run
sudo vim v and have that happen for free. Global aliases are almost always more trouble than they're worth, so I don't recommend that, but depending on your usage patterns some global alias might be convenient (I'd recommend a longer and more unusual name if you do: putting some odd punctuation in can help avoid running it by mistake, so
alias -g v# ... or
^v or something).