warm up to (someone)

Translations
проникнуться симпатией к (кому-то)
It took a while for the new cat to warm up to us.
Потребовалось некоторое время, чтобы новая кошка прониклась симпатией к нам.
Definitions
To gradually become more comfortable with or start to like someone, often after an initial period of hesitation or uncertainty.