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First, go to Settings - General - Keyboard - Keyboards, and make sure “Emoji” is there. If you can’t find it, add it again.
If it is there:
Try restarting the iPhone, and if that doesn’t help, force restart it.
To restart, turn off your iPhone and turn it on again.
To force restart your device, press and hold Home and Power button simultaneously until you see the Apple logo. As soon as it appears, let go of both buttons. The iPhone will power up on it’s own.
The icon on the key changes to a globe when you have more than the usual keyboard and emojis installed. When you tap the globe key, you’ll find the Emoji keyboard again.
Hope that helps.