Not an expert, but if your tree is grafted, any branches coming out of the ground should be cut off as these will not produce the same fruit as what your peach tree is. They will also take over the main graft. Hopefully the reason the main trunk has no leaves is because it's going dormant.

Thank you for your reply. I had a feeling the 2nd branch coming out of the ground shouldn't be therte but was reluctant to cut it off before getting advice. The tree shouldnt be dormant as it is spring.

As long as the grafted portion is still alive I wouldn't worry overmuch. I'd trim anything under the graft and give the tree time. I've always been told that peach trees have super growth in spring-summer but my limited experience in spring planting has been that they were pretty slow to establish the first year.

I hope it is still aliv e. I trimmeed off the 2nd branch coming out.