She was starting to get a feel for the new office.
Literal
She [topic-は] new office [possessive-の] feel [object-を] grasp-begin was.
感じをつかむ ('to grasp the feel of') is a set expression for developing an intuitive sense of something. つかみ始める uses the ~始める auxiliary to mark the onset of this understanding. The ~ていた places us in a narrative past: she was in the process of settling in.