Once a captain has nominated his players to one of the umpires, that nominated team cannot be changed without the consent of the opposing captain. If such a change is made, the new player is often referred to as being a replacement. The Law does not use that term nor does it say anything to suggest that the new player takes over where the previous one left off; for example, it could say that he should not bat if the player he replaces has batted. It does not say that, though that may well be a subject of discussion before consent is given.
If there is a change in the nominated team, the originally nominated player can take no further part in the match other than, perhaps, to act as a substitute. The 'replacement' player can take a full part. He can bat bowl, keep wicket, etc, subject to any restriction imposed as part of the agreement between the captains that resulted in the consent being given.
In some major competitions, replacements are allowed by right when a player is taken from a team in order to play representative cricket. That leaves his original side a player short; often a replacement is allowed there as well. In these cases, and also when the replacement is a super-sub, he takes over from the player he replaces; for example he can bat only if the replaced player has not completed his innings.