Thanks so muchHi and welcome!
Do you have space to set up both cages simultaneously?
If so, you can put the new cage next to current cage. Try place one of the toys or items from current cage in the new one. Start slow! Allow the bird time to check it out at their own pace.
Maybe add some new, interesting items in new cage that they can go check out in their own.
Place some of their favorite treats in food bowls to encourage them to go inside.
Then you can start serving meals inside the new cage.
Slowly (as in one or two items every few days) begin moving items from old cage to new one until they've become comfortable and accepted new. Give them as much time as they need to adjust, even up to a couple weeks if possible.
I'm sure others will have tips as well.