Just replaced an old cast iron sink with a stainless. Also put new drain pipe and trap. It now drains slow unless the garbage disposal is on. It did not happen with the old one . Can't figure it out.

Sounds like you might have disturbed some trash built up in the pipe walls and now you have a partial blockage. Remove the trap and send a snake up into the wall, There will be a 90 about 8" in but once past that you only have 6 more feet to go.

Flush with a tub full of hot water. Good luck, Tom

Is the new sink deeper than the old sink?