Her father, Jevrem was the first man in Belgrade to introduce Western European customs and manners into his home; he also owned an extensive library.

She went on to have her writings published in a variety of periodicals, including the literary journal Danica ilirska, in which she used her pseudonym, "An Illyrian woman from Serbia".

[1] Croatian poet Antun Mihanović, who was the Austrian consul in Belgrade and a frequent visitor to her father's home, fell deeply in love with her and sought her hand in marriage.

[2] Anka invited the most prominent artistic and intellectual women in Belgrade, as well as the wives of foreign diplomats to her celebrated salon, which featured musical performances along with readings of Serbian, French, German, and Italian poetry.

Sometime after her husband's death, Princess Anka and her daughter, Katarina were invited by her cousin Prince Mihailo to live at the royal court.

On an unknown date, Anka gave birth to an illegitimate daughter by her former brother-in-law, Jovan Ghermani, who was the husband of her late sister, Simeona, who had died in 1837 at the age of 19.

[7] The Serbian newspapers announced her death with the obituary: "With his Royal Highness, his cousin Mrs.[nb 1] Anka Konstantinovic was also killed".

As Princess Natalija was Anka's granddaughter, thus a descendant of the Obrenović dynasty, the Serbian government promised that should Alexander die childless, which seemed likely after Queen Draga's false pregnancies and encroaching age, the crown of Serbia would pass to Prince Mirko.

Following the brutal assassination of King Alexander and Queen Draga by a group of Army officers led by Captain Dragutin Dimitrijević Apis on the night of 10/11 June 1903 (by the New Style calendar),[9] the crown instead passed to Peter Karađorđević, who was viewed as pro-Russian, while the rival Obrenovićs were known allies of the detested Habsburgs.