Kitty Maitland, a friend of Laura('s) and a party guest, is....
Is the possessive case necessary in the above sentence?
If LAURA is replaced by HER, then we must say a friend of hers.
May I have your opinion?
Yes but we should explain to our students that this is idiom, an exception to grammar. A friend of me or or a friend of Laura may well appear to them to to be correct, rather than a friend of mine or a friend of Laura's.