That leaf looks like it comes from some kind of oak tree. Like maybe a live oak? (But apparently there are many species even of live oaks). So, ... "Quercus something-us"
It isn't clear if your big tree - or your little tree - has leaves that look like that. Or is it both?
That last option seems most likely to me. It looks like the little tree is suckering off of the big tree. It has sprouted out of the root where the root was exposed to the air.
If that is the case, I wouldn't call the small tree a "parasite", because it is a part of the larger organism. (The bark of the two trees looks a lot different, but that might be because of the youth of the little tree-stem.)
People refer to these little trees sprouting from the root of the main tree as "suckers", and if they are caring for fruit trees, they trim the suckers off because they take nutrients from the main (fruit bearing) part of the tree, and they make for a messier growth pattern, etc.
If what you have is indeed an oak tree, you probably aren't worried about fruit production, but it will cause your tree's profile to be scrubbier and less neat/elegant. If the two trees appear to be the same organism (same leaf type, etc.) I say go ahead and prune off the sucker.