Complex sentence: Initially assigned to Vice, she is desperate to be transferred to Homicide, and after Tom Matthews promotes her she starts to grow self-confident, relying less on Dexter's abilities and more on her own.
Split into simpler sentences: Initially assigned to Vice, she is desperate to be transferred to Homicide. After Matthews promotes her, she starts to grow self-confident, relying less on Dexter's abilities and more on her own.