For most people with an ICD, moderate resistance exercise including bench-pressing is not ruled out, but there are important considerations depending on when you were implanted and what your underlying condition is.
In the weeks immediately after implantation, lifting heavy weights is restricted. Sudden forceful use of the pectoral muscle on the side of the device can place stress on the lead before it has fully bedded in, and your clinic will give you specific guidance on arm and shoulder movement during this initial period. Most people are asked to avoid raising the arm on the implant side above the shoulder or lifting anything heavy for four to six weeks.
Once fully healed, whether you can return to weightlifting depends largely on your underlying condition rather than the device itself. High-intensity exercise raises heart rate significantly and in some conditions this can increase arrhythmia risk. Your cardiologist is the right person to advise on what intensity is safe, and an exercise test may be used to assess your individual response.
There is also a practical consideration with heavy pressing movements: repeated significant pressure directly over the device site, or any exercise that causes the device to shift or become uncomfortable, should be discussed with your clinic. A protective vest or pad may help in some situations.