It's an example of a reduced relative clause
A reduced relative clause is a relative clause that is not marked by an explicit relative pronoun or complementizer such as who, which or that. An example is the clause I saw in the English sentence This is the man I saw. Unreduced forms of this relative clause would be "This is the man that I saw." or "...whom I saw." Wikipedia
EDIT 15/03/23
(Many thanks to @Stef in the comments) I hadn't considered the fact that F.Scott Fitzgerald would have used be to form the perfect with the intransitive verb ‘come’ in “a nightingale is come over on the Cunard…”. Although The Great Gatsby was published in 1925, nearly a hundred years ago, I wasn't aware this construction, at least in American English, was still in use at the time and some native speakers would consider ‘come’ in ‘come over’ as an adjective.
Dictionary.com says [emphasis mine]
- (used in archaic or literary constructions with some intransitive verbs to form the perfect tense):
He is come. Agamemnon to the wars is gone.
Wiktionary offers this quote from Shakespeare's Macbeth, 1601
- They are not yet come back.
instead of the modern They have not yet come back.
From the 1722 novel, Moll Flanders, by Daniel Defoe; we have two examples of the perfect tense used in the same excerpt.
but at his Defire I altered that Resolution, and he is come over to England alfo, where we refolve to spend the Remainder of our Years in fincere Penitence for the wicked Lives we have lived.
From The Tenant of Wildfell Hall written by Anne Brontë in 1848
I went down to dinner resolving to be cheerful and well-conducted, and kept my resolution very creditably, considering how my head ached, and how internally wretched I felt. I don't know what is come over me of late; my very energies, both mental and physical, must be strangely impaired,…
In The Great Gatsby quotation, the modernised version would be:
…that I think must be a nightingale [which has] come over on the Cunard or White line
The relative clause with a present perfect construction could be replaced with ‘having’
…that I think must be a nightingale having come over on the Cunard or White line.