The sentence, as you wrote it, comes across as incomplete. I read it as "She was Queen. She would abdicate". We would need, for example, an IF at the end to tell us if this was in the past or is in the future, and if it happened (or not) or if it will happen (or not). It becomes a conditional clause, it's the would/could/should depending on context.
To use Italian as an example, and some of the the modal verbs in Presente (in Indicativo/Condizionale tense);
Lei vuole.. (Hon vill..| She wants..)
Lei vorrebbe.. (Hon skulle vilja..| She would like..)
Lei può.. (Hon kan..| She can..)
Lei potrebbe.. (Hon skulle kunna.. | She could..)
Lei deve.. (Hon måste.. | She must..)
Lei dovrebbe.. (Hon borde.. | She should..) *Note that 'skulle' becomes 'borde' here.