GOV.UK
ATA carnet procedures: animals born of animals under an ATA carnet
Once completed an ATA Carnet cannot have additional items added to it.
(Istanbul Annex A Article 5 (3)
EU issued carnets
Animals born in a third country while the mother has been temporarily exported under an EU issued ATA carnet cannot be added to the carnet. On arrival in the EU, they must be declared for import on a C88 (SAD) (HMRC website) and all import duties paid.
Third country carnets
Animals born in the EU while the mother has been temporarily imported under a third country ATA carnet cannot be added to the carnet. The young must be declared for export in the normal manner on C88 (SAD). No export refunds are permitted.