masraf çıkarmak, masraf doğurmak, masraf açmak

[Tureng-Çağla]

?

[Tureng-Özgür]

put sb to expense

Their visit put us to a lot of expense

[eastender]

to run expense

[ALI-KARABULUT]

at sb's expense
a) if you do something at someone's expense, they pay for you to do it
　- Her mansion was refurnished at taxpayers' expense.
b) if you make jokes at someone's expense, you laugh about them and make them seem stupid or silly
　- Louis kept making jokes at his wife's expense.