。
She's been holding a walking stick the whole time.
Literal
She [topic-は] hand [in-に] walking-stick [object-を] the-whole-time is-holding.
ステッキ is a loanword from English 'stick' (walking stick/cane). ずっと (the whole time, continuously) emphasizes the duration — she hasn't put it down. 手に~を持っている is the familiar pattern for holding something. The ずっと adds a sense that the speaker finds this notable or that it's been going on for a surprisingly long time.