At the EU level, there are efforts to ban leaded ammunition not only for hunting but also for sport shooting. Possible effects for sport shooters would be:
Lead has a very high density. If one wants to produce bullets of the same weight from other materials, they must have a larger volume. However, since the diameter of bullets must remain the same due to the caliber, only longer bullets can be used. Either it is more difficult for the manufacturers to keep the caliber dimensions at all, or the larger bullet has to sit deeper in the case, which means less space for the propellant charge - overpressure can occur during ignition. Longer bullets are also more prone to "spin" due to the leverage that is applied to them during free flight-so they require a tighter twist to compensate. So there is a risk that existing guns with longer bullets will have less accurate shooting performance. Alternative materials tend to be harder than lead- this leads to increased barrel wear.
Finally, lead-free ammunition is often much more expensive than ammunition with lead bullets- for average hunters who shoot 1-2 boxes of ammunition per hunting season, the premium is hardly significant. Sport shooters sometimes shoot thousands of rounds per season, which means that a lead ban can raise costs to a level that threatens their very existence.