at someone's expense
US /æt ˈsʌm.wʌnz ɪkˈspɛns/
UK /æt ˈsʌm.wʌnz ɪkˈspɛns/

1.
a expensas de alguien, a costa de alguien
paid for by someone; causing loss or damage to someone
:
•
The company party was held at the company's expense.
La fiesta de la empresa se celebró a expensas de la empresa.
•
He made a joke at her expense, which made her feel uncomfortable.
Hizo una broma a su costa, lo que la hizo sentir incómoda.