Collocations for carrot - noun

raw
cooked, steamed
baby
chopped, diced (esp. BrE), grated, shredded (AmE), sliced

eat, have
cook
peel
chop, dice, grate, slice

top
cake
juice
stick

dangle, hold out, offer (sb)
They dangled the carrot of a large salary in front of me.

a carrot and stick
to adopt the carrot-and-stick approach