“ihres” would be the genitive case. You also use it when you want to say “of her father”.
“The car of her father” = “das Auto ihres Vaters”
“Of her father” is also translated as “von ihrem Vater”. If you are using the word “von”, then it comes with the dative form which is “ihrem”.
If you are, however, not using “von”, then you say “ihres”.
1) Her husband’s book/The book of her husband = Das Buch ihres Mannes/Das Buch von ihrem Mann
2) The judge’s decision/The decision of the judge = Die Entscheidung des Richters/Die Entscheidung von dem Richter
3) The dog’s owner/The owner of the dog = Der Besitzer des Hunds/Der Besitzer von dem Hund
4) His professor’s office/The office of his professor = Das Büro seines Professors/Das Büro von seinem Professor