Claudius reveals his fears in the following lines of act 3, scene 3:
“What if this cursed hand
Were thicker than itself with brother’s blood
Is there not rain enough in the sweet heavens
To wash it white as snow?”
His fears are connected to the murder of his brother and the consequent punishment he perceives as a real curse.
Detailed answer:
The fears of Claudius are conditional upon the awareness of his guilt. He awaits the curse to fall upon him as it seems to be a logical extension of killing his brother. At the same time, he still has a hope to escape this punishment. However, such an outcome does not seem to be possible, and the thoughts of its inevitability bother him.
Claudius can do nothing but pray in the chapel, unwilling to leave the hope for forgiveness. He is overcome with the thirst for power and the expressed remorse, and none of these feelings seem to win. This situation represents him as a man full of doubts despite the violence and decisiveness he demonstrated by the act of murder. In these lines, he seems to be a manipulative but weak person.
However, even remorse does not change the desire of Claudius to kill Hamlet. The risks are not only in losing power but also in losing his life. The manipulations of Claudius finally result in the expected outcome. This circumstance strengthens his thirst for power and puts aside any considerations of guilt and punishment, which usually follows. Nevertheless, such success is only temporary, and he will be punished for his actions.