NACI does recommend that people who have had infection should be vaccinated.
They have recently come out with some suggestions with regard to the time period between infection and vaccination. They have said if you've had an infection and you haven't yet completed or started your primary series—your first few doses—you should wait eight weeks from that infection to get the first or second dose of your primary series. That's to allow that infection to help mount a good response from the infection, but then to enhance it with a vaccination, because we know that protection from infection can be variable. If you have a mild infection, you may not mount as good an immune response. We know that for protection against omicron, if you've had an omicron infection, you don't mount a very good immune response against other types of COVID-19, against other variants.
It is very important to be vaccinated after you have been infected, but NACI recommends these intervals. They suggest to wait eight weeks for your primary series, and then for your booster, they suggest to wait three months between the infection and your booster or at least six months between your primary series and the booster, whichever is longer.