Dyskaryosis refers to changes to the cervical cells. The HPV virus is a risk factor for it but not the only cause. HPV is often a dormant virus, 90% of adults will have it at some point, but only in those who are sexually active. This is why children are now vaccinated against it as there is no treatment other than the body managing it.
In those who have it, most resolve within 12 months due to the body immune response, no treatment is necessary, other than only to the cervical cells if they change.
It is not considered a sexually transmitted disease in this instance. You or your partner can have it as a dormant virus, it can take years to appear. Therefore it is not suggestive of you or your partner having other partners, but more often an indication of previous sexual partners (from years before).
You do not need testing for this, it is routinely checked with each smear. There is a form of HPV which causes ulcers and lesions, this is a different form. If you were to have these then yes you should have sexual health screening. It is unlikely to reappear again, but a new partner could re-introduce it. Either male or female can be the carrier.
I hope that this helps.