Thermal compound is already on the component, but it is usually always recommended to get an extra thermal compound with better specifications.

I used the Thermal Grizzly Kryonaut (12.50 W/m K, 1 g) for the 11900k, which is known for rather high temperatures. The results are surprisingly good. The AIO used there in the Lian-Li vision case is https://www.digitec.ch/de/s1/product/lian-li-galahad-ii-trinity-performance-360-cpu-wasserkuehler-41385924.

At the moment I am building another PC with LGA 1200 socket. The case is NZXT H7 Flow (2022). For this one I will use the Kraken 360 RGB, also with the Grizzzly Kryonaut thermal compound. CPU as in the Intel 11900k above. I'm curious to see the temperature difference.

Same CPU and thermal paste. Case and AIO are different. I will publish the results in a Community article if the community is interested.

It it already applied but id recommend you to remove it and add new because it is very little applied

No is available on the AIO