From Longman Dictionary of Contemporary Englishthe thrill of the chase/huntthe thrill of the chase/huntthe excitement you feel when you are trying to get something that is difficult to get, especially when you are trying to get a romantic relationship with someone → thrill
Examples from the Corpus
the thrill of the chase/hunt• A strange feeling of expectation mixed with our fear as we became caught up in the thrill of the hunt.• Was it just the thrill of the chase?• But it is not every image that succeeds in suggesting something of the thrill of the hunt as well as curiosity. 