I just captured a sylesti yesterday night and i still don't get the ability to get new party slots. Can someone help please? Is this a quest?

To get a second party slot, you need to go to esior's haven plaza and buy a second slot. A third slot can be bought once you unlock the second region, umbra forest and go to the sanctuary.

i did goto william the hunter and it still says i need to capture a sylesti

Hmm... I think you need to finish the "capture a pet" quest. Did you use a trap to catch the pet, or was it a triggered event? Cause the quest is a triggered event that occurs when you explore, and doesn't require you to actually use a trap.

If you've completed the quest (ie found a pet), you'll need to open the satchel you received as a reward for the system to register that you've completed the quest.

I used a lesser snare trap i bought from esiors haven.

Yeah... I don't think you completed the quest yet. You have to keep exploring until you trigger an event where you meet a pet, and they ask if you want to capture/keep it. Something like that.

thx