Hard to say from the info you've given. In general the re-use of a string of letters is not a problem if the words the letters appear in have different meanings. But I'm guessing from your question that the pun you are applying to Player is to make the meaning like "one who plays" and, if that's so, I think it would not be acceptable to have "play" elsewhere in the puzzle. But again, I'm just guessing from what you've said above.
Good luck with the puzzle!