We appreciate the sensitive nature of this question.
First and foremost, it is important to note that urinary incontinence can often be improved and even resolved through urogynecological physiotherapy. We urge any woman with occasional (or more chronic) incontinence to explore this possibility in order to improve her situation and avoid further deterioration.
It is permissible to engage in ritual activities, such as reciting prayer or blessings, with a wet or even saturated pad, as long as the urine cannot be smelled. If the pad has an odor, it should be changed prior to performing a religious ritual.
To the extent that a woman can feel distinct urination or leaking, she should wait until it finishes before ritual performance, or pause in the middle.
Note that a woman with incontinence may wear a liner or pad during the clean days, but these should be white to leave open the possibility of noticing niddah staining. She should continue to wear white undergarments under the pads, since they may shift in place.
Please write back with any further questions.