Answer by taking a quote from the following article:

Supergirl is a fictional superhero appearing in American comic books published by DC Comics. The character was created by writer Otto Binder and designed by artist Al Plastino. Supergirl first appeared in a story published in Action Comics #252 (May 1959) titled "The Supergirl from Krypton". Kara Zor-El is the biological cousin of Kal-El (Superman).

After long-time Superman family editor Mort Weisinger retired in 1971, the character underwent revitalization under editor Joe Orlando and artist Mike Sekowsky. Wearing a series of new outfits, leaving her adopted foster home with the Danvers family, Linda goes on to San Francisco where she works for KSF-TV as a camera operator and develops a crush on her boss, Geoffrey Anderson. These stories introduced Supergirl's most memorable villain from this period: Lex Luthor's niece Nasthalthia, or Nasty. Nasty had made two appearances towards the end of Linda's college years, then pursued her to KSF-TV, trying to secure proof of her dual identity.  Supergirl starred in her first solo eponymous monthly series beginning in 1972 until October 1974, when her monthly title merged with Superman's Girl Friend, Lois Lane, and Superman's Pal Jimmy Olsen to produce a new title: then-highest DC selling series called The Superman Family, where she eventually became the steady lead story. Linda worked as a student advisor at New Athens Experimental School, before leaving for New York to follow a career in acting with daytime soap Secret Hearts.  In 1982 Supergirl received a second monthly solo series titled The Daring New Adventures of Supergirl, relocating the character to Chicago as Linda became a mature student of Psychology. Industry legend, and former DC Publisher, Carmine Infantino provided the pencilled art (Bob Oksner inked). With issue 13 the title was revamped, with a new costume design (sporting a red headband) and the title shortened to just Supergirl. The series ran until sudden cancellation in 1984, only two months before the character's debut in a big-budget Hollywood film starring Helen Slater.  In the Crisis on Infinite Earths (1985) the greatest heroes from Earth-One, Earth-Two, Earth-Four, Earth-S, and Earth-X join forces in order to defeat the Anti-Monitor. When Superman comes face to face with the Anti-Monitor and is knocked unconscious, Supergirl rushes to save him before he is killed. She is able to fight him off long enough for Dr. Light to carry her cousin to a safe distance, but is killed by the Anti-Monitor. A public memorial service for Supergirl takes place in Chicago, where Batgirl (Barbara Gordon) delivers the eulogy. In her remarks she states "Kara is a hero. She will not be forgotten." Superman then gives his late cousin burial by taking her corpse to Rokyn/New Krypton to Zor-El and Allura. A Superman issue the next month reveals that Kara had experienced a premonition about her own passing. However, when the universe is rebooted, the timeline is altered. Kara Zor-El and all memory of her is erased from existence.

what happened during the bronze age
the character underwent revitalization under editor Joe Orlando and artist Mike Sekowsky.