No it’s not necessary to repeat the subject pronoun (or the subject in general), however if there is an object pronoun, you’ll have to repeat the full verb. Your example would be:

J’ai préparé un repas et l’ai mangé.

As mentionned by Stéphane, you could also skip both the object pronoun and the auxiliary, but that would result in a slightly different meaning.

J’ai préparé un repas et j‘ai mangé.

(meaning “I cooked a meal and ate”, a bit different from “I cooked a meal and ate it”), would be shortened to:

J’ai préparé un repas et mangé.