Italicizing a Title Which Includes a Ship Name
This is a question of style, not grammar. You would write that in accordance with whatever style guide you are to follow, whether it be MLA, APA, Chicago Manual of Style or something else that your teacher or school has provided.
In general, I've seen three ways of handling it:
- merely italicizing "Essex" with everything else, thus it not being set apart from the rest of the title in any way†;
- super-italicizing it, if available (i.e., a more extreme form of italics with a steeper slant than the italics already being used);
- underlining "Essex," underlining generally being the standard of any style guide when italicization is unavailable, like it's how people used to style book titles when typing as typewriters usually didn't have an italics option, so by underlining the name of the ship, you are indicating additional italicization to the italicization already being used.
So, if you're not beholden to any particular style guide or the style guide you are beholden to is silent on this issue, you would be falling within common practices doing any of the above.
What you should not do is not use italics and merely return to standard text. Now, you might be able to get away with that if "Essex" weren't the last word in the title, but since it is, since no italics would appear immediately afterwards to sandwich it in to the title, what you would end up with is a last word that simply falls out of italics, thus appearing to not be part of the title or appearing to be a mistake. It's kind of like how it's normal to capitalize the first letter of the last word of a title no matter what it is, even if it's a preposition, prepositions not otherwise taking a capital first letter in a title, as making the last word look different has a tendency of making it appear to be not part of the title or making it look like a mistake.
† Probably the most common (e.g., https://en.wikipedia.org/wiki/Essex_(whaleship) - see ref. 3).