In creative writing, any imaginable tense mismatch is "allowed" as long as it fits the context. However, your sentence is odd because there is no context to explain the mismatch. If this is a typical past-tense narrative, then it makes no sense to use the present tense without justifying the use of the present tense in some way. For example:
A tree stood in the middle of the plain, the kind of tree around which children like to play
In this case the present tense makes sense because the description of the tree is timeless. It's not saying that children are playing there, merely that they might choose to play there now and then.
Note also I changed it from "the children" to just "children". The definite article specifies a particular group of children who exist in the the time frame of the standing tree. In this case it's confusing to talk about them in a timeless way, because it's not clear from the limited context when or where they exist.
Assuming this is a typical narrative in either the present or the past tense, then then tenses should match:
The tree stands/stood and the children play/played around it.
It is possible to write a story in which the time frame is all jumbled, where you might mix past and present tenses in clever ways. But this is not typical, difficult to do well, and likely to confuse the reader.
In more formal, expository writing, you should avoid clever writing tricks like this, as your goal is either to inform or persuade, and anything that might confuse the reader will usually detract from this goal.