肝(かん) (kan, “liver”) + 腎(じん) (jin, “kidney”). 心 is a daiyōji replacing 腎; the じん (jin) reading of 心 is not an example of rendaku.

• IPA^(key): [kã̠ɲ̟d͡ʑĩɴ]
• (Tokyo) かんじん [kàńjíń] (Heiban – [0])

肝(かん)心(じん) • (kanjin) -na (adnominal 肝(かん)心(じん)な (kanjin na), adverbial 肝(かん)心(じん)に (kanjin ni))

1. (figurative) vital, essential, main
   • 2017 December 1, 宮本徹, quotee, “第195回国会　衆議院　財務金融委員会　第2号　平成29年12月1日”, in 国会会議録検索システム‎^[1], 国立国会図書館:

     都合が悪くなると、ほかのところは詳細に覚えていても、すぐに肝心なところは記憶がないで逃れる。

     Tsugō ga waruku naru to, hoka no tokoro wa shōsai ni oboete ite mo, sugu ni kanjin na tokoro wa kioku ga nai de nogareru.

     When things get inconvenient they immediately shirk responsibility by claiming they can't remember the crucial points, even though they can remember other details perfectly.

肝(かん)心(じん) • (kanjin) 

1. (figurative) that which is essential or fundamental

Prior to the addition of the character 腎 to the Jōyō Kanji List in 2010, that character was substituted with 心, producing 肝心. The new standard recommends 肝腎 instead, but 肝心 is still more widely used.

• “肝心”, in 漢字ぺディア [Kanjipedia]‎^[2] (in Japanese), The Japan Kanji Aptitude Testing Foundation, 2015–2026

From 肝 (chimu, “liver”) + 心 (kukuru, “heart”).

肝(ちむ)心(ぐくる) (chimugukuru) 

1. thoughtfulness, sincerity