For this arc, I really hope either these situations will play out:
1) Cesar brings Canaria along and they win the war together. She’ll help with tactics etc and both return with impeccable reputation supported by the people in order to overthrow the Empress/Parlams
2) While Cesar is at war, Canaria becomes a villainess and rises in the political/high society circle through scheming to stop the Empress/Parlams and secure loyal vassals who will help secure Cesar’s position as Crown Prince