I am a TC Controller at LTCC. This is what I would expect for jets.
In the climb, on departure, 220kts(ish) max climb power through the level given. If already climbing normally at normal speeds, again full power and reduce the speed to increase climb rate.
In descent, if given a speed restriction, use the brakes and mantain the speed given. If there is no speed restrition, fly the plane to comply with the request using speed and/or brakes as appropiate.
I would expect most jets to give me at least an extra 1000 to 2000 feet in either direction. More if you are a GTI jet
Obviously this does not apply to heavy (weight) aircraft on departure but at least go for max power and try, even if it is only an extra 500'/min.
If in doubt ask!
Many Controllers say '' best rate''. What does this mean? Best economical rate for the aircraft or expedite for ATC. They should always say 'expedite'