Family members are usually possessed in English. So the best translation is probably "She's there with her sister."
If there are two brothers and two sisters, then one of the brothers could say "She's there with our sister" or maybe "She's there with sister."
"She's there with a sister," could sound like she's with an African-American woman.
95% of cases the meaning of this sentence in Ukrainian is "with her sister", "her" is omitted because it's assumed the sister is hers.
Another meaning could be, "with the sister" (assume she has several sisters, one sister was mentioned earlier, so we refer to her as "the sister")
"With my sister" -> mmmm nah. We would say "з моєю сестрою", omitting possessive with family members works only with "mom" and "dad" in Ukrainian. Maybe it used to be a thing before, but not anymore.
"With a sister" -> what is it even supposed to mean?....