There is exactly one situation in which an embarked Admiral would take command of the ship, and that is if the CO is killed in battle, in which case regulations dictate that the highest-ranking command-eligible officer becomes the CO.
Even in that situation, the admiral is going to relinquish command to the XO 99% of the time, as the admiral does not know the ship, or her crew. As well, the admiral is still in command of the battle group, and is not going to burden themselves with giving orders to the bridge crew.
Alas, real life is not analogous to Star Trek, or any other Naval show/movie, really. It’s just not exciting, and doesn’t make for good hollywood fodder.
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