From Longman Dictionary of Contemporary Englishprice on somebody’s headprice on somebody’s headSCCGIVEa reward for catching or killing someone → price
Examples from the Corpus
price on somebody’s head• He was also unusual among philologists in having had a price on his head.• As a soldier under the Whites there was a price on his head; some one would soon discover his true identity.• Bream often have the biggest price on their heads but roach, rudd and hefty tench can provide a healthy bonus. 