As the Silver Age waned DC went through the first of their periodic shake ups to revitalise their characters. But unlike later attempts, this was not any kind of co-ordinated event, as it required no retconning, and each editorial team within the company took a different approach.
For Supergirl this involved an intermittent depowering similar to what was happening to Superman at the same time, but more importantly it involved her quest for a new costume. Kara had been wearing the same old dress since 1957. It had never gone out of fashion because it had never been in fashion, but changing it was a big deal because at this point in history no established superhero had ever changed the design of their costume (Wonder Woman doesn't count, since she stopped wearing hers altogether). DC promoted this with a big competition among the readership of Adventure Comics, and in Adventure #397 she got a new outfit designed by Diana Prince (Wonder Woman), though I'm not sure I'd be taking practical fashion tips from a woman whose idea of clothes fit for street fighting and action adventure were exclusively coloured white.
Despite the announcement that Supergirl would now be seen in a variety of fan-designed costumes it would be a year before she changed again (Adv #407), when the scientists (scientists?) of Kandor had finished running up a wardrobe full of monstrosities.
For reasons unknown, Kara's first choice of the scientist designed costumes is one of the worst. The red tights were apparently a colouring mistake (who would know?) since they are changed to blue in the next issue. Sadly, the pixie boots remain and one can only assume these were done on purpose.
Of course the new costumes had the advantage of remaining invulnerable even when her powers faded, which came in quite handy when she got dunked in acid in #407, so it makes you wonder what the thinking was behind the backless, sideless, sleeveless, legless number she wore in #409.
In Adventure #410 she first wears the hot pants number that would see her through the 1970's, and although she continues to try out alternatives until #415, this is the only one that recurrs.
It was only changed again in the 1980's for the Olivia Newton John cheerleader look that she died in fashion-wise long before Crisis.