What is one example of a high ranking person speaking in rhyme in Act 4 of Hamlet?
You might find it useful to consider the ending of scenes. Shakespeare often uses rhyming couplets in his blank verse to round off scenes and effectively close them before beginning a new scene, so if you have a look at the scenes in this act and consider which ones are ended by the speech of a high ranking character, you will probably find the example of rhyme you are looking for. Consider, for example, the way in which Claudius ends Act IV scene i with the following lines:
Come, Gertrude, we'll call up our wisest friends;
And let them know, both what we mean to do,
And what's untimely done. O, come away!
My soul is full of discord and dismay.
Note the rhyme of "away" with "dismay" and how this emphasizes his depth of turmoil and internal emotions after discovering that Hamlet has killed Polonius. This serves to highlight his fear that he might be next now that Hamlet has shown him that he knows of his involvement in his father's death through the play that he put on for Claudius.