First a rider .... I haven't flown the A320 family since 2005.
From my recollection, I found the Expedite function in climb very useful. It promptly applied CLB thrust, whereas not using it resulted in CLB thrust taking 5 or more seconds to be applied.
So, if asked by ATC to expedite, I would set the new cleared level and push EXPEDITE and then shortly after CLB thrust had been established, pull selected speed and adjust as appropriate, reducing towards Green Dot or whatever seemed appropriate - it's not rocket science folks.