Teeth are able to move on their own, without any orthodontic force being applied, whatever your age. The most common natural movement is all the teeth gradually moving forwards over the years under pressure from the tongue.
If a single tooth is missing, you may notice the teeth next to the gap starting to move towards each other and tilt. This is due to the network of fibres in the gum that connects the teeth and pulls them towards each other.
It is important to note that this natural movement does not happen with wisdom teeth. If a wisdom tooth is extracted, the other teeth will not move backwards, because there is nothing for them to be pulled towards.
When teeth are moved backwards with orthodontic force (for example, to make use of the space freed up by an extracted wisdom tooth), gaps can appear between the teeth further forward. This is because this kind of movement usually happens in groups rather than one tooth at a time, which can lead to the space being distributed unevenly.
This answer is for general information. Your own case needs an examination by an orthodontist.