If your judgement is based on the fact that you have no brood and are unable to visually spot the Queen it doesn't mean that you are Queenless.
There may be a non laying Queen or a virgin Queen in there.
The marking paint may have been cleaned off the old Queen.
If you put a new Queen in there and it is not Queenless the bees will kill the new Queen.
Your other post suggests that there are a lot of bees in the hive, I think you estimated 50,000.
Wait till we get another warm day (15c or above), and take another look. Ideally get another beekeeper to take a look - fresh pair of eyes.
If still no Queen then add a frame containing eggs from another colony - if it is Queenless the bees will build Queen cells from this, in which case you can then decide to try adding a Queen or leave a Queen cell to hatch.
Beekeeping takes a lot of patience.