"Моя дочь смотрела этот фильм, а я ещё нет."
Translation:My daughter has already watched this movie, but I have not yet.
The «а» calls for a contraposition, so «еще нет» in one part implies its opposite «уже» in the other. However, there is no particular reason why it is omitted in the Russian sentence, you can put it back if you want (before «смотрела»).
If in this case I were the father rather than the mother, would it be necessary to use смотрел in the second half of the sentence, rather than just sharing the verb from the first half. Or is it simply understood that if the same basic verb is being used but for different genders twice in the sentence, one can leave it out the second time?