an iron hand in a velvet glove
US /æn ˈaɪərn hænd ɪn ə ˈvelvɪt ɡlʌv/
UK /æn ˈaɪərn hænd ɪn ə ˈvelvɪt ɡlʌv/

1.
a person who is outwardly gentle but inwardly firm and unyielding
:
•
The new manager has an iron hand in a velvet glove; she's polite but gets things done.
•
Despite his gentle demeanor, the CEO ruled the company with an iron hand in a velvet glove.