No, not in normal circumstances. Your ICD is programmed to deliver therapy only above a specific heart rate threshold, set well beyond what ordinary vigorous exercise produces. Raising your heart rate through exercise will not trigger an inappropriate shock.
Your device clinic takes your activity levels into account when programming the device, so tell them if you are returning to running, cycling or other demanding exercise. If you are ever shocked during or after exercise, stop, rest, and contact your device clinic or cardiology team the same day so they can review what the device recorded.
Most people with ICDs exercise regularly and without issue. The bigger barrier is usually confidence rather than the device itself, and that improves with gradual, consistent activity.