I had a permanent retainer in that broke causing one tooth to have a gap. I was told a retainer could fix this?

It depends, what kind of retainer were you referring to? A Hawley removable retainer? Sometimes they can add wires or springs that can help move the tooth. Probably a better approach is find a dentist/orthodontist who can do Invisalign. Possibly just one or two aligners to get your teeth back into position, and then they can do a removable Invisalign retainer for you to use (called a Vivera retainer) which works very nice.

Retainers by definition "retain" and not move teeth. Depending on how far your teeth moved apart it may or may not be possible to correct with removable appliance (not a retainer, but kind of like it). The appliance is called "spring aligner", the other possibility would be "invisalign-like" treatment with 3-5 aligners.

Permanent retainers, do not last long due to the masticatory forces. Ff it broke go see your orthodontist, there are many types of retainers that can just readjust it and then you can set again a permanent one, this will help your doctor, to see how the treatment has evolved.