Old iphone's whatsapp conversations?

My old iphone's screen is black and won't work. It receives calls and vibrates though so the phone is not broken, just the screen. Meanwhile I got another and put my simcard in it. I was wondering if when the old iphone gets its screen fixed, but my simcard is not in it, there's any chance that the conversations that I've been having on my new iphone will be there, or even the ones that were there before I took out the simcard. I wanna know this for whatsapp and iMessage conversations. Please if anyone knows the answer I'd really appreciate it it's important.

Yes. WhatsApp messages are stored on the phone, not the SIM. SIMs don't hold much of anything these days.

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