You said you have a missing tooth! Ideally The tooth will require to be replaced either with implants or fixed prosthesis. But you say the gap is only 3mm . In that case you may opt for veneers or crowns depending on your case. Orthodontically even if you close this gap it will not look esthetic cause there will be no symmetry between teeth on left side and right side . This is because if you observe your front teeth each tooth looks different, it’s shape ,size. So even if u go for orthodontic treatment you will need esthetic correction in the form of veneers or something later.
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If you could post a pic I would be glad to help you more.