carrot and stick

the carrot and (the) stick (approach) — кнут и пряник

tаkе / use a carrot and stick approach to sb (reward and punish someone at the same time) — применять политику/тактику кнута и пряника по отношению к кому-л.

If you use the carrot and stick approach, you persuade someone to try harder by offering them a reward if they do, or a punishment if they do not

Example: The emphasis is on the carrot of incentive rather than the stick of taxes. (OALD)