These spaces in gums are called periodontal pockets. If the pocket is not very deep then a deep cleaning and root curettage(treating the root surfaces) might give you some relief and cause the pockets to be treated completely. However, you will have to visit a periodontist for a complete periodontal therapy as this might require long term maintenance from your side. A periodontist can guide you as to how to take care of the gums once the treatment is done so that the problem doesn't recur.

Kindly post pictures or x ray of the tooth.

It could be a periodontal problem . Difficult to give a treatment plan without clinical examination.