Enter edit mode for sudoers.
Add the following at the bottom.
Defaults:nagios !requiretty nagios ALL = NOPASSWD: /usr/sbin/exim
And thats that.
Normally defaults requiretty is set earlier in the file, which stops sudo from running while not under a tty (shell) we override this for nagios user by setting defaults:nagios !requiretty as showed over.
Visudo is a command for opening /etc/sudoers in your distros default editor.
NOPASSWD does so command does’nt need password to run sudo.