What I want to is unpack this a little bit, starting with the intentions of Israel's enemies in the prophecy:
O God, do not keep silence;
do not hold your peace or be still, O God!
2 For behold, your enemies make an uproar;
those who hate you have raised their heads.
3 They lay crafty plans against your people;
they consult together against your treasured ones.
4 They say, “Come, let us wipe them out as a nation;
let the name of Israel be remembered no more!”
Psalm 83 opens with a plea asking God to no longer remain silent, peaceful, or still. Now notice God's silence in the last two millennia, post-Pentecost. He has been very audibly and visually absent from the world stage.
The next several verses describe what Israel's enemies are up to and what their intentions are. Throughout history many have undertaken to destroy Israel and her people: several Pharaohs, Assyria, Babylon, Haman, Greece, Rome, Caliphates, Spain, Hitler, etc. They've had varying "reasons" for doing so: fear of Hebrew overpopulation (Pharaohs), land and plunder (Assyria and Babylon), vengeance (Haman), rebellion (Greece and Rome), religion (the Caliphates and Spain), and hatred of Jewish ethnicity and presence in Europe (Hitler).
Of course, all of these attempts have failed because God is with His people. Israel will never be destroyed.
Notice, though, the reasoning given in Psalm 83 for destroying Israel: it isn't any of the above mentioned reasons. The reason is to simply "wipe them out... [that] the name of Israel be remembered no more!"
What reason has Iran, Hezbollah, and Hamas been giving for destroying Israel? Religion is a key motivator, but what they are continuously saying is:
"Wipe Israel off the map". This exact phrase has been routinely used and with great frequency. Additionally, the Ayatollah in Iran has recently said their reason for destroying Israel will be to make them "forgotten from the pages of history". The object of their attack is not specifically "the Jews" (as was the case with many previous enemies like the Pharaohs, Haman, Spain, and Hitler), but is usually cited as "the Zionists"... i.e. the specific Jews living in the nation-state of Israel.
The hatred of the specific nation of Israel is the reasoning behind Iran's, Hezbollah's, and Hamas's intentions. They say they want to "wipe Israel off the map" and make "[Israel] forgotten from the pages of history". This appears to be a clear alignment with the enemies in Psalm 83.
The next question is: who does Psalm 83 say these enemies are?
the tents of Edom and the Ishmaelites,
Moab and the Hagrites,
7 Gebal and Ammon and Amalek,
Philistia with the inhabitants of Tyre;
8 Asshur also has joined them;
they are the strong arm of the children of Lot.
Byblos and Tyre = Lebanon = Hezbollah (all of southern Lebanon).
Philistia = the Gaza Strip (controlled by Hamas)
Assyria = Syria, Iran, and parts of northern Iraq
Ammon, Amalek, Moab, and Edom = Jordan and possibly Egypt (Edom extended over parts of Egypt and it has been surmised that the Amalekites took control of Egypt after Ahkenaten's death in the Red Sea)
This war will definitely include Lebanon, Gaza, Syria, Jordan, and Iran. It may also include Egypt, Iraq, and Saudi Arabia, depending on how one defines the boundaries of Edom, Assyria, and the Ishmaelites/Hagrites.
Please thoughtfully consider this article: http://www.debka.com/article/22378/Hamas-signs-binding-military-commitment-to-Iran-led-war-on-Israel
There now exists a binding military pact between.... Hezbollah, Hamas, Syria, and Iran.... that is Lebanon, Gaza, Syria, and Iran. The purpose of said military pact? To destroy Israel. The only missing piece is Jordan. And possibly Egypt, Iraq, and Saudi Arabia, but their involvement in the prophecy is not certain.
Having said all this, it is also quite possible that Psalm 83 has already been fulfilled: either in 1948 or 1967. I would wager on 1967 as all the necessary enemies mentioned in Psalm 83 were present.