A 1k monarch exp is an item in Evony TKR (The King's Return). It can be found after killing certain monsters or bosses, with some of them listed below.
The description of 1K Monarch EXP in Evony TKR says:
Use it to gain 1,000 Monarch EXP.
1K Monarch EXP is known to drop from a number of bosses or monsters upon killing, including Witch, Golem, Lava Turtle and Warlord.
Note: This list may be incomplete.
1K Monarch EXP is known to potentially be obtainable from opening Junior Hydra Chest and Medium Hydra Chest. The links for each item are below:
Note: This list may be incomplete.