As the captain, it is your call and you should have a discussion with him. I bowled with a guy last year that joined our team in mid-season and he was horrible about it and didn't seem to respect the time of everyone else. There were nights when the entire league was finished bowling and we were only on the 5th or 6th frame of the last game. A league came in after us and whoever got our pair would have to sit around and wait for us to finish. We became "that team" that everyone on the next league had to wait on and I had enough of it. I talked to him first, but he was friends with the captain and didn't care so I went to the secretary and asked if I could join another team instead. After a league vote that allowed me to transfer teams, I was happier about it, but as luck had it the first night I bowled with my new team our opponent was...you guessed it...my old team. Oh well, at least I was happier getting off that team.
Fast forward to the beginning of the season league meeting this past summer and several of us spoke up about instituting a rule that if you were up, you bowled, regardless if the rest of your lineup was still bowling on the opposite end. It isn't enforced as well as it should be, but if we have a complaint we can go to any of the officers and they will put them on notice. If it continues, the officer can no score them for a frame, but as far as I know it hasn't happened yet. Doesn't do much about the slow bowling, but at least it keeps the pace moving better this year.