There is a Hitching Post add-on.
One I believe is a "replica" can be made by Tinkers (IIRC), and can only be recharged Twice.
There is also one that can be bought in the in-game UO Store with sovereigns (Sovereigns purchased via origin dot com) that might be rechargeable more than twice. (not sure)
Unlike stabling at a stable (where you only get charged when you stable), using the hitching post uses one charge for stabling, and another for claiming.
If you go into the dungeon below Blackthorn's castle, there is an in-game equivalent hitching post that can be used by players to call in their pets (As the castle is a no-pet zone - pets autostable when they enter the grounds)