For players with Pass already, Accurate is the best skill for increasing their success at passing and also has a couple of other benefits as well.
Listing of all the passing skills in the game and an explanation on their best uses as well as which players to bear in mind to select them on.
Dump-Off lets you try and retain possession of the ball if your ball carrier gets hit, though some caution is advised to not drop the ball needlessly.
Leader has become a passing skill under LRB5, read this on its application and which players to consider it with.
Pass allows a player to reroll the ball when making a pass which not only increases the chance of success but saves team rerolls.
Safe Throw is a very handy skill to have on your teams Throwers, with two useful abilities both of which retain possession of the ball for your team.