Apple - iPhone - How to set up not requiring passcode if recently closed

I believe the setting you are looking for is Settings > Touch ID and Passcode > Require Passcode.

It should be noted that using a Microsoft Exchange account in email can effect the options available here. For example the only option on my phone is "immediately". this thread is how i finally learned why I only have the option "immediately".

You have to disable Touch ID for "iPhone Unlock" on newer iOS devices in order to set a time to lock your phone. In Settings > Touch ID & Passcode, disable (toggle off) Touch ID for iPhone Unlock. Once toggled off, you can then change the time to require passcode by accessing the "Require Passcode" option.

Basically it sets to "immediately" only with Touch ID enabled for unlocking your phone.

1. Open the Settings App and navigate to General –> Passcode Lock.

2. To set the passcode lock delay, locate the button where you see Require Passcode. By default you will see “Immediately” next to Require Passcode. This means that as soon as your device locks, your passcode will be enabled. If you want to delay this, tap on the button and select After 1 minute, After 5 minutes, or After 15 minutes. When you select any of these three time intervals, your device will not require you to re-enter your passcode for the relative time you selected.