Do you provide your consent as this child's parent or guardian for them to have access to website?
This is a sentence appeared on website, but I am confused about the sentence structure, in the as clause, they dont have a verb, and dont make clear what is the consent to.
That is because "as" is not introducing a clause in this case. The meaning is "Do you, as the child's parent or guardian, consent that the child have access to this website."
Formally, it involves an ellipsis: "Do you, [in your legal capacity] as the child's parent or guardian, consent ..."
It is not a well written sentence.
There is no as clause; as is being used as a preposition here. As Collins has it, meaning four applies:
You use as when you are indicating what someone or something is or is thought to be, or what function they have.
The sentence you quote could be rewritten as
Do you, being this child's parent or guardian, provide your consent for the child to have access to the website?
An as statement to indicate that someone is being, speaking, acting, etc. in the capacity, role, condition, etc. of something is very common; you may have seen formulations like
As a taxpayer, I demand to know why this road is still not repaired.
