Karamu is basically a large dark blue version of Kurama (Red Nine Tails). He wears a grey chakra mask and has two heads on each side of it's main one. Each of those made of Chakra and only appear when Karamu gets seriously angry. He has dodgerblue/white stripes on his tails as well.
Karamu is usually kind to those who treat him as such. He uses the chakra mask to scare other tailed beast from fighting him. He dislikes fighting unless the object it is fighting has lots of hatred because Karamu dislikes hatred. He is basically almost the opposite of his variation, Kurama.
The relationship between Karamu and Shizaku is similar to that of B's and Eight Tails's relationship. As a kid, Shizaku would "dream" a lot and would talk with Karamu. At first, Karamu scared Shizaku, however as Shizaku got to know Karamu, they began to like each other. Once Shizaku got older he would always fall asleep in the academy when he was bored so he would be able to talk with Karamu. However, Shizaku is not completely able to control the power of Karamu. Karamu would gladly lend his power to Shizaku, as long as Shizaku promised not to overuse his chakra. There is also a chance that the Chakra may engulf Shizaku, and Shizaku would go on a rampage because he was not able to control the chakra. Meaning he can only use so much of it before losing control. As a kid he trained with his father to control the tailed beast as much as possible. So Shizaku was able to control up to two tails, before loosing control. And as of right now that is the maximum he is still able to control.