Learn Spanish (Latin America): Ella está alegre hoy.

This is a simple statement describing a feeling using the adjective alegre (cheerful). You only trigger the subjunctive when a verb of emotion is followed by que and a change of subject. For example, me alegra que ella esté aquí (I am happy that she is here). Here, we are just stating her current mood directly without a second clause.

Why do we use está instead of es here?

Alegre changes meaning depending on the verb. Using estar describes a temporary mood or state: she is feeling cheerful today. If we used ser (ella es alegre), we would be describing her permanent personality: she is a naturally joyful person.

If the subject is ella, shouldn't the adjective end in 'a'?

Not all adjectives change to match gender. Adjectives that end in -e in their base form, like alegre, triste, or inteligente, are gender-neutral. They stay the same for both masculine and feminine subjects. They only change when pluralized, becoming alegres.