A <em>linking verb </em>is a type of verb that describes the subject by connecting to the predicate in the sentence. Since it serves as a connector, this type of verb does not refer directly to an action as a regular verb would.
In this example, the word "have" serves as an auxiliary verb for the verb in present participle "been". The link of both these words make for the linking verb which conects the subject "Shelly" and the predicate "more careful on the path".
<em>Should </em>is not part of the linking verb; it is a modal verb.