For most words that end in <ite> the pronunciation is aɪt. However, here are some words for which the pronunciation is ɪt:
apposite exquisite favourite granite hypocrite opposite preterite requisite
The word respite can be be pronounced either as ˈrespɪt or as ˈrespaɪt. The second of these is probably more common these days.
The word composite is generally pronounced ˈkɒmpəzɪt (or sometimes kəmˈpɒzɪt). However, with the specific meaning of “A composite resolution put before a Trades Union Congress, which has been compiled from several related resolutions proposed by trade unions or constituency Labour parties” (OED) the pronunciation is ˌkɒmpəˈzaɪt.