
can anyone check this sentence, please

I've adopted. This Japanese sentence is correct.

※「生き甲斐」は「生きる楽しさ。張り合い」

The word is still a bit cloudy to me. Can I use the word "életcél" (life aim) if I translate this?

I'm not sure (because it's in English), but I think it's good.
生き甲斐(いきがい):
- reason for living(生きる理由)
- one's life's purpose(人生の目的)
- what makes one's life worth living(人生に生きる価値を与えてくれるもの)
- motivation for living(生きる動機)
- live for ...(…のために生きている)
参考URL: https://eikaiwa.dmm.com/uknow/questions/971/
どうかな?

seems similar, but if you do not have "életcél" then it is not the end of the world, you can find an another aim, a purpose for living