My child is scared of making mistakes near our goal

I would first make it clear that she is not required to take the same risk in every part of the pitch. Playing with confidence does not mean refusing to clear the ball near your own goal. The useful question is whether she is choosing the clearance because it is the best option, or because fear has removed every other option before she looks. In training, give her lots of small games starting near goal where there are two sensible solutions: one safe pass or carry, and one clear-away option if pressure is too high. Then praise the decision, not whether it looked brave. I would also be careful with adult reactions when it goes wrong. If one mistake gets a huge touchline response, children learn very quickly that mistakes near goal are different. Help her see risk more clearly rather than asking her to ignore it.