Translation:She finally got a position of power.
Adding to my previous comment. "secured" the position might be the most accurate, though not exactly as colloquial as "got." However, the alternative answer given by Duolingo, "earned," should not be correct because it implies that she actually earned it, say, by an accomplishment, rather than obtained it. Since we don't know why she was able to get it, "earned" should not be a correct answer.
Whether it's intentional or not, on September 4, 2019, there's a feministic leaning in the first three examples of "poder" on this page:
Examples of "poder" "Ella finalmente consiguió una posición de poder." "El rey perdió su poder." "Ella tiene todo el poder."
We should encourage one another and build each other up (1 Thes 5:11.) You'll receive power when the Holy Spirit comes upon you (Acts 1:8.) You'll be exalted when you humble yourself (Matt 23:12.)