First, let me be clear that I believe Andrew Whitworth will be the Bengals' starting left tackle on opening day and I also believe he will be back to a Pro Bowl level again this year. But Whit is currently the oldest starting left tackle in the NFL right now so the topic of his eventual replacement will be pressing this draft and certainly more so as time goes on. Anthony Collins could have been the successor but he certainly wasn't going to wait around making backup money when a team like Tampa Bay was willing to pay him $6M/year already.
So how does this impact the Bengals' draft plans? I would expect them to try to land a high ceiling player in the second round if possible (I think it's almost a given the Bengals go corner in the first due to overall age in the secondary and the injury status of both Newman and Hall). Personally I'd prefer Antonio Richardson (Tennessee) at pick #55. He's built like a prototypical left tackle (6056, 336, 35" arms) although his shuttle times are concerning (20yd 5.06, cone 8.10) it matches closely to Whit's times as a draft prospect. Mel Kiper projects Brandon Thomas (Clemson) to us in the 2nd round but at 6032/317 he would be the shortest LT in the NFL by one inch! I just don't see this pick making sense unless it's to play LG.
What if the Bengals wait for later rounds? Interestingly enough 75% of all current starting left tackles were drafted no later than pick #73. It doesn't mean you can't find a starting left tackle after that (in fact the highest rated tackle based on average value is Jason Peters who wasn't drafted) but the probability is very small. If in fact the Bengals don't draft someone in the first two rounds, look for Newhouse to be Whit's backup this year and OT be the major focus in next year's draft.
By the way, it's easy to forget how talented Whit was coming out of LSU. He didn't get much pre-draft publicity but his measurables were terrific. At 6070/334 he had a 30 1/2" VJ and a 9'4" broad jump. This would rank him 4th and 3rd respectively in this year's OT/OG class.