Choose the option that best completes the gap(s) We have known Rose for some years now, she is a friend of ____

The correct option to complete the sentence is "ours".

Here's the explanation:

• Ours: This is the correct possessive pronoun. It is used to show ownership and does not require an apostrophe. It means "belonging to us". In the sentence, "she is a friend of ours" effectively means "she is a friend belonging to us".
• Our's: This is incorrect because there is no possessive pronoun form with an apostrophe before 's'. Possessive pronouns are inherently complete and do not need an apostrophe.
• Ours': This is also incorrect. The placement of the apostrophe after 's' suggests a plural possessive, which is not applicable here.
• Our: "Our" is a possessive adjective and must be followed by a noun to make sense in a sentence. The phrase would be ungrammatically incomplete if constructed as "she is a friend of our".

Therefore, the correct choice is "ours" because it properly shows possession without the need for an apostrophe.