elder sister
姊 centers on the concept of an elder sister, a female sibling older than oneself.
姊 combines 女 (woman) with 牙, which likely contributes the sound and may relate to the idea of seniority or order. The exact historical development is uncertain.
A woman 女 beside 牙, which looks like a tusk or fang, suggesting an older, more experienced sister who protects like a tusk.
For シ, imagine your elder sister saying 'she' is the one who always looks out for you: 'she' -> シ.