This can be very difficult
By "Travelled Queens", I generally mean those that have been bought from a commercial source, not come from yourself or another beekeeper where the queen has been laying in the last day or so. A queen that has recently been laying is likely to be accepted reasonably well if the usual precautions are taken, but a queen that has been off-lay for some time may be difficult to introduce.
When you buy a queen you don't know anything about her. The chances are she is imported and has already had a lengthy journey, including getting to the airport, at least one flight, then getting to you, which could have been via a dealer. The queen could have been in transit several days and without water all that time.
Queen rearers don't know how many queens they are going to sell or when they will be required. A common way of keeping them until they are needed is to "bank" them. Queen banking is where a number of queens, perhaps a minimum of 50 up to 200 are placed in cages and put in a colony that will look after them until they are needed. There are different techniques involving both queenright and queenless colonies. I have seen accounts of queens being banked for 6-8 weeks and sometimes overwintered. I have no experience of banking, other than keeping the odd queen in a cage in a super for a short time. Not only do queen rearers bank queens, but apparently some dealers do too.
The queen you buy could have been recently laying, or perhaps not for several weeks. That together with any trauma caused by travelling is unlikely to do the queen any good, so she probably won't be in as good a condition as a home reared or sourced queen. It is little wonder that travelled queens are often very difficult to introduce.
To have the best chance of introducing a travelled queen I suggest doing the following:-
The queen can be introduced into a larger colony once she has been laying for at least a full brood cycle.
It is a personal view that queens that are raised from stock that are not adapted to the area will not usually perform well. This is not only in productivity terms, but in other areas such as toughness and wintering. Before purchasing queens from a commercial supplier that may have been reared several thousand miles away, I suggest you think very carefully about the possible result of your actions.