Welcome back to Eorzea fellow Meteor Survivor!

Mounts in ARR are gained via a consumable item that 'unlocks' them, so for the 1.0 Gobbue mount if you transfered your 1.0 character that you had gained that mount on into ARR you should start ARR with a Gobbue Horn item in your inventory (if it's not in your inventory, find a special NPC in one of the three cities called a 'Calamity Salvager' - they store extra items that may be missing from your inventory (because ARR's inventory was reduced from the size of 1.0's one, so the Calamity Salvagers act as a kind of 'inventory overflow' for that).

Either way, find the Gobbue Horn item and use it and you'll have the Gobbue back.