If you need a trainer in Morrowind visit Train House

Interesting. UESP also list trainers. But there are some oddities. For instance it lists Urjorhad in Ashalmimilkala shrine as training Alteration, Mysticism and Restoration, although he is decidedly defunct from the beginning of the game. He obviously didn't use restoration on himself! It also lists all those smugglers, daedra worshippers and outcast Ashlanders who attack you on sight. Since you'd have to calm them every time you wanted to train a level who would bother?

What neither of them shows is the level to which they train.

Also, off topic, I think it is little irritating that certain skills can only be taught to maximum if you belong to a faction (Speechcraft, Security, Conjuration). I know you can 'keep practising' but certainly in the case of security this takes a long time. Are there even enough locks to pick or untrap?

if you want to level up on security buy a lock spell and buy some lockpicks. This takes a long time but if you really want your security skill up it will work.

also if u need a trainer for security there is one in aldruin(sp?) but only if u really need it and if ur securtiy is below 50 because with trainers (or in my experience) once a skill is past 50 they usually cant train u anymore i know for a fact it is with security the trainer is in the rat in the pot