Getting a new phone with straight talk?

Can I just buy a new phone and put the SIM card in that? I have an older iPhone. I have the 5se and I'm getting the 6 or 7.

Yes, if the phone is unlocked.

I bought a Galaxy S9 directly from Samsung. I told them that ATT was my provider. So when the phone came in the mail, it also came with the SIM card. When I plugged the card into the phone, that activated my account with ATT on the new cell phone.

Took me about 30 minutes to activate my account on the new S9. Easy to do.