According to Dr Sharib:

"Al-'Adl is the One Who is ever just and equitable. He does not
perpetuate tyranny nor does he inflict hardship. The people cannot
understand His ways."

Emulation of the name requires voluntary submission to the Will of Allah,
unbegrudging acceptance that whatever comes is best. Also to be just, in
word and deed, and dealings with people, without having feelings of
superiority. It also requires one to be moderate in everything.
"Moderation is the key to success"

Appropriate invocation enables a person to overpower and dominate
others and thus requires to be 'properly' used.

see 'The 99 Most Beautiful Names of Allah' by Dr Zahurul Hassan Sharib



Some other references:

Al-Ghazali says that justice implies that in the universe all things are in
exact proportion and in the correct place and situation, as they should be
- nothing is amiss.

Al Ghazali describes it thus:

"So whoever wants to understand this attribute must comprehend the
actions of God Most High from the kingdom of heaven to the end of the
earth, to the point where one does not notice any fault in the creation of
the infinitely good One, and turns again and sees no rift in it, yet turns one
more time only to have his sight become weak and dulled; for the beauty
of the divine presence has overwhelmed him and bewildered him with its
harmony and its regularity: for such a man something of His
justice......clings to his understanding."

In the case of man's share in justice it implies that things are done that
are appropriate to the requirements of the situation. It would not be justice
for a generous donor to give money to the wealthy or arms to scholars.

He emphasises the importance of ruling our own nature justly, in other
words of putting passion and anger under the guidance of reason and
religion.

(Al-Ghazali - The Ninety-nine Beautiful Names of God. Trans. Burrel/Daher: ITS: 1992.)


Consideration of this attribute is associated with our coming to
understand that even imperfections partake of the perfection of God's
creation.

One can think of it also like this, that not even a leaf falls except as it
should do.

It requires us not to be critical, even of criticism.

JMZ
Bismillah ir Rehman ir Rahim
Al-'Adl
The Just
The Equitable One