The Wales fullback is struggling with an achilles injury this season.
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Parker said: "We're probably looking at a few months for Connor, which is not ideal. It's a big setback for us but hopefully he'll come out the other end of that.
"There was an issue in and around his achilles that we thought we could maybe manage a little bit, there were some more conservative options, which we went down the route of and Connor did to try and get back, and that hasn't seemed to work.
"So we've had to now get to that point where we've made a decision to get this fixed."