No, the act of making a claim on your supplemental critical illness insurance does not directly cause an increase in your premiums. Premiums are primarily determined by factors such as your age, health condition at the time of policy acquisition, and the level of coverage chosen. However, keep in mind that premiums may be subject to adjustments over time due to factors like inflation or changes in your age category. It is advisable to review the terms and conditions of your policy to understand how premiums may change in the future.