From Longman Dictionary of Contemporary Englishcarrotcar‧rot /ˈkærət/ ●●● S3 noun 1 
[countable, uncountable]HBPDFF a long pointed orange vegetable that grows under the ground grated carrots carrot juice2 [countable] informalPERSUADE something that is offered to someone in order to try and persuade them to do something They have refused to sign the agreement despite a carrot of £140 million.3 → carrot and stick
[countable, uncountable]HBPDFF a long pointed orange vegetable that grows under the ground grated carrots carrot juice2 [countable] informalPERSUADE something that is offered to someone in order to try and persuade them to do something They have refused to sign the agreement despite a carrot of £140 million.3 → carrot and stickExamples from the Corpus
carrot• Governments were forced to adopt a carrot and stick approach to the trade unions.• Add chopped carrots and garlic and cook 2 minutes.• Cook carrots according to package directions; drain.• She dipped her carrot into the peanut butter as she went to the door.• Boil the carrots in a saucepan until tender.• One of the carrots that Dad always dangled in front of me was that he was going to send me to college.• The U.S. has held out the carrot of more aid and investment.• The carrot and stick approach is to do with reward and punishment, incentives and pressures.• This time you need the top two centimetres from a thick carrot.• You can sow these directly into the ground in April, along with carrots and parsnips.Origin carrot (1400-1500) French carotte, from Late Latin, from Greek karoton 