Getting Clicks but no Impressions seen in GSC
If you are getting Clicks but no Impressions in your Google Search Console reports then it is probably due to the fact that your visitor clicked on the page as the result of an Impression for a related page.
Normally you will see far fewer Clicks that you get Impressions reported. The fact that there are those that are searching for this behaviour means that I am not the only one seeing this in my GSC reports.
Google Search Console help files do not mention this and are not much help in understanding what is going on here.
Getting Clicks with no Impressions or Queries
It is also possible to get Impressions with no Queries and Clicks with no Impressions.
While the Search Console tool is probably the most useful tool that a webmaster can have it has to be remembered that it will only report data that is captured by Google. If a search was made using another search engine the result recorded by GSC will only be that received by Google. For example, if an Internet user makes a search using Bing and then clicks on your page and you have Google tracking on that page, you will see a click recorded but will not see that there was an Impression corresponding to the search.
Impressions without Queries is a little more difficult to explain. However, users of Google Anaytics as well as Googel Search Console will also be aware that Google most commonly does not report the search query in the GA reports. Please see my page on "not-set-not-provided".