。
She'll attend the meeting in my place.
Literal
She [topic-は] me [in place of-の代わりに] that meeting [to-に] will-attend.
~の代わりに ('instead of X / in X's place') is the standard substitution pattern. With a person, it captures going somewhere or doing something in someone else's stead. The ~でしょう ending marks future probability or expectation — softer and slightly more polite than a flat assertion. 出席する ('attend, be present at') takes its event with に. The whole sentence has a measured, slightly formal feel suited to professional or official contexts.