On my forum IPB v.3. we have sponsors who have their own forum section and they have limited moderation rights in that forum section only
is there a way to assign a member moderation rights to specific forums in IPB 4 ?

I've looked all around acp but don't seem to be able to do this

Hey @Jelly Belly™ - yes you can 

 

Members --> Moderators (under staff) --> Add Moderator

You'll have to remove all permissions and then there should be a tab for "forums" which you'll be able to select which forums you when them to have the mod rights to there. 

 

Hope this helps