A rumor spreads through defence.pk forum couple of a years ago. But still there's nothing loud to confirm by the appropriate authority. However, it could be very possible because of the higher threat assessment for navy. Till today, if Pakistan Navy needs air support they must call air force. But considering the situation and multi-front scenario they could think of an fighter arm of Pakistan Navy Air Arms.
Due some speculation and information from highly valued sources of the forum it can be assumed that really navy going to establish their Naval Fighter Regiment soon. If this happen still we need to wait to see the real.