A normal trademark will not work internationally, it will not be protected in a foreign country. A trademark is territorial, and an application must be filled in in every country that protection for that trademark is sought.
If it is an international trademark search you are doing to check if a trademark has already been taken, we recommend you search if there is even anything similar, by doing this you may prevent any difficulties in the future that may appear.
When doing an international trademark search, firstly check the countries that you are hoping to get your trademark registered in, some companies will do a free initial search for wordmarks and can compile you a report on an international trademark search, a search like this could save you potentially hundreds of pounds and not to mention time (a normal trademark application can take up to 6 months and can still then be rejected)
An international trademark search can find out if someone already holds the rights to something you may want to trademark.
When doing an international trademark search, you can be expected to pay anything from £450 up to £1200 depending on what part of the world you want the trademark application to go to. If you contact a decent trademark company, they will have all this to hand and be able to quote you a price before you go ahead with the search and application. The time it takes to come back can also vary depending on what country you are applying the trademark to be set up in, some can take 3-4 months, others up to 13 or 14 months, unfortunately, an international trademark can take the latter.