I did what you said, added A record and it says now
sport 178.79.145.163 Default
and my virtual host is like
<VirtualHost *:80>
ServerAdmin
marko@arabba.hr
ServerName sport.arabba.hr
ServerAlias
www.sport.arabba.hr
DocumentRoot /srv/www/sport/public_html/
ErrorLog /srv/www/sport/logs/error.log
CustomLog /srv/www/sport/logs/access.log combined
</VirtualHost>
But when running sport.arabba.hr i get page not found, did enable the site and it is in sites-enabled. Is part of directory being only "sport" wrong, should i put sport.arabba.hr as document root, do I need to adjust some NS settings?