Generally no, but if you have an unstable bite, especially one with a deep overbite, or have tongue habits that push on your teeth, the gap could open up over time. There are two ways to help try to prevent this. One is to wear a retainer. The other is to have your dentist bond the teeth together from the back of the teeth (called splinting, or fixed lingual retainer).
Will my gap in my two front teeth open up after bonding?
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Movement of teeth after bonding is possible without a retainer
The likelihood of your front teeth shifting after bonding depends on the cause of the original spacing. Some patients have very stable bites, most do not. The only true way to ensure your teeth do not shift from the current position is to either have a small fixed wire retainer placed behind your teeth, or to consistently wear a nighttime retainer to sleep after the bonding.