If I should die, please donate my heart to someone who needs it.
Literal
By-chance I [subject-が] die-[conditional-たら], my heart [object-を] necessary person [to-に] donate-[polite request-て下さい].
提供する ('to provide, to donate') is a formal verb commonly used for donations, services, and contributions. 必要な人 ('a person who needs [it]') is a compact relative clause — the na-adjective 必要 ('necessary') attached to 人 with な.