Is there an option or way to make the 'Online Application' link disappear for users once the user has signed in && has a minimum rank that determines whether they are a member or not ?

No there isn't. But that is probably a decent idea to add to the show for rank x and higher argument to add the option to only show for rank x and lower. I was looking at a solution I posed to another operator for hiding the gallery link when your not a site member but that does the opposite of what you want as it follows the show for rank x and higher option. In order to accomplish what you desire you would need to use the Advanced Layout options and have some form of javascript I believe to make it work.

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Six Demon Bag
Jack Burton: Hey, what more can a guy ask for?
Egg Shen: Oh, a six-demon bag!
Jack Burton: Terrific, a six-demon bag. Sensational. What's in it, Egg?
Egg Shen: Wind, fire, all that kind of thing!

Chops I think this idea has a lot of merit. We often think of content we want to conceal if your not a member or not a certain rank and higher but there is not functional opposite in the system. Unless I am missing something I don't see an option to filter for if you are not a member of the site or you are a specific rank or lower. I recall some posts with stuff like this before but I don't remember the topics to readily find them via the search.

--
Six Demon Bag
Jack Burton: Hey, what more can a guy ask for?
Egg Shen: Oh, a six-demon bag!
Jack Burton: Terrific, a six-demon bag. Sensational. What's in it, Egg?
Egg Shen: Wind, fire, all that kind of thing!

heres a topic from some time ago:

http://www.dkpsystem.com/viewthread.php?threadid=2446&p=1#p8195


but that is only for seperate parts not for a link in some specific menu so it's not doable to hide that specific link atm

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designer of http://aszune.dkpsystem.com

Actually...

With advanced layout you can just reproduce the Main Menu and include only those links you want (after all Main Menu links to specific locations and isn't really dynamic).

I'll be adding some kind of <!--System:IfRankElse-->

As well as <!--System:IFNotRank:X---> and <!--System:IfnotRankElse-->

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It's all in the reflexes.

It is even easier than that and if implemented by Chops the way I am thinking and describing would be done entirely without an Advanced Layout for those that are not web savvy.
In the Basic Menu Administration you can remove the Online Application from the Main Menu.
Then if you go to Static Menus and Content you can create a separate menu for the Application and make the link to the application so that it opens in the main page when clicked.
you would need Chops option the IfRankElse to hide the menu from members though or change the options on the Static Menus and Content page to allow for a show to rank X and above or X and below assuming the mechanism was built such that if you chose Everyone there is no one below everyone so only non members would see it. Or just make a Hide from members option.

--
Six Demon Bag
Jack Burton: Hey, what more can a guy ask for?
Egg Shen: Oh, a six-demon bag!
Jack Burton: Terrific, a six-demon bag. Sensational. What's in it, Egg?
Egg Shen: Wind, fire, all that kind of thing!