Bad recommendation letter from previous postdoc adviser I am completing my first postdoc and I had a pretty bad experience with my current adviser. I finally got to publish something, contribute in a grant writing etc., but overall it hasn't been great... 

Now, I am going to start a new postdoctoral appointment under the supervision of a faculty I have been working with for several years and I will apply for tenure track positions once this last appointment has ended. I am pretty sure that my new adviser will be able to provide very good recommendation letters for me in the future. So the question is, will I need to provide recommendation letters from my current adviser? What if those are not good?
When applying for your first tenure track job most search committees will expect that your PhD supervisor and current supervisor will be amongst the N letters of recommendation that you provide. While having your PhD supervisor and current supervisor write letters is not a strict requirement their absence would be noticed. The other letters can come from anyone that knows you well and is experienced enough to write letters for a TT position. There is no expectation that you have letters from all supervisors that you worked with.

That said, you should talk with your current supervisor about the possibility of getting a letter. There maybe some positions they are willing to recommend you for and there may be cases where you need N+1 letters and you only have N.