Based on the Latin text provided, Sicilia (“Sicily”) would be in apposition with insula (“island”), and both would be declined in the same case—in this case, nominative. Clara (“famous”) would be the predicate adjective (or subject complement) of the subject insula.
The translation would be, “The island Sicily is famous.”
This idea could also be expressed by means of a genitive (a.k.a. “appositive genitive”), viz., Clara est insula Siciliae. One such example of this “appositive genitive” is found in Jerome’s Latin translation of Acts 8:5:
Philippus autem descendens in civitatem Samariae praedicabat illis Christum
Edit: @fdb does raise a plausible objection regarding “the city of Samaria.” However, the appositive genitive does occur elsewhere in classical Latin. For example, in Aeneid of P. Vergilius Maro:1
Hic tamen ille urbem Patavi sedesque locavit Teucrorum...
Nevertheless, here he settled the city of Patavium2 and the seats of the Teucrians3...
(Patavi is the genitive declension of Patavium. If urbem were in simple apposition, we would expect Patavium, which is also declined in the accusative declension like urbem, rather than the genitive Patavi.)
Admittedly, such a construction is rare, and as others have stated, it is more common to encounter the city and the name of the city in simple apposition (rather than in a genitive of apposition).
Virgil. The Bucolics, Georgics, and Aeneid of Virgil: with English Notes. Ed. Moore, Edward. Boston: Sanborn, 1857.
1 Book 1, Line 247 (p. 87)
2 or “Padua”
3 or “Trojans”