The sentence is almost correct but could be clearer with a small adjustment: "Do you have old clothes you'd like to give?" This revision is more grammatically correct and flows better.

It depends somewhat on the context, but 'and like to give' doesn't seem to make sense, or is not the best way of saying it. If you're asking a person if they want to give away old clothes, you want something like: Do you have old clothes you'd like to give away/donate?

Your sentence is grammatical but is confusing because it appears to express two thoughts that have no connection, such as in this sentence: "Do you have old clothes and like to swim?" Clearly having clothes and liking to swim are unrelated thoughts. Your sentence is not quite that bad, but it is close because it does not create any relationship between having clothes and liking to give. You must create that relationship: "Do you have any old clothes THAT you would like to give?"