Just thought would point out that even if you don't ask for advice from the planning office about your proposed extension, and just put an application in, the planning officer should still come round to do a site visit once you have submitted the application. So the planners are pretty likely to spot the tree at some point.
They could put a tpo on it at any point as well; before an application is submitted or after.
But as others have pointed out it might or might not be worthy of a tpo, trees usually have to have public amenity value for one to be put on, or it might not be very healthy. The council might also have a tree officer who the planners may ask to look at the tree to see if worthy of tpo. Also the extension may or may not affect the tree or it may affect it but still be ok to do the extension.
My neighbours have just built a two storey garage (there's a room in the roof) v close to a protected tree - think six feet. They had to have the foundations specially assessed, but got permission easily enough.