I currently have a propane dryer
I am buying a new gas dryer
Will I need a conversion kit to prop[ane or will current gas connections work on new dryer?

Yes, you will need a conversion kit. See if it can be ordered with the kit installed.

The gas and vent connections will not likely be in the same place, so unless the supply lines are flexible, you may have installation issues.

"Identical connections in the same place"is not likely.