I applaud you Anthony. Very valid

As far as a security force goes, maybe pattern it after Japan's Self Defence Force. They also act as the nation's law enforcement agency. They are charged with keeping the peace amongst citizens and with the defence of the nation as a whole.
This would, might maybe, could fulfil the portions of the Constitution that discuss security and protection of Asgardian citizenry as a whole, as well as any long-term residents or visitors.
An alternative might be to make all adult citizens responsible for ensuring overall peace and tranquility... A citizen's obligation.

This, however, is just my opinion. Now, let wiser heads prevail.

I agree with many stated above, as a nation, we do need a military or a security force, like Japan's Defense Force. I agree with CodeOperator, when we eventually build space stations or off-world bases, the Asgardian government needs security to protect those stations/bases. Aside from physical and asset security, and transport security, we need to protect our government officials, so that card's on the table as well. So if not a standing military (strictly for defensive purposes), we would need to establish security forces---and in all aspects of the word too; information/cyber security, physical security, and so on. As William Zimmer said above, we would need training and policies in place for disgruntled employees/rogue agents.

Being part of a newly-formed nation, I'm excited to see what we can conceptualize on this topic.