As far as I know, "authoritarian" is mostly used to describe the power itself ("an authoritarian ruler", for example). However, are there any similar word to describe someone who wants/need an authority to function properly?
Someone who needs or requires some authority figure in their life can be referred to as a "follower" (as compared to a "leader"). This is not necessarily a negative, although it has some negative connotations.
His whole life he had been a follower -- he never sought out a leadership position and always avoided the spotlight.
A more negative way to say this, for a group of people who act as followers, is to call them "sheep".
You lot are just sheep, always nodding your heads and agreeing to whatever your candidate says. Don't you ever think for yourselves?
A more positive way to express this is "disciple", meaning someone who follows a leader in order to learn from them.
The popular yoga teacher went everywhere with a group of disciples in tow.
There are other words as well, just look up the synonyms of "follower".
Can you find what you are looking for in these words?
Subservient suggests one who craves someone to direct them.
3 : obsequiously submissive : TRUCKLING