ICAO Doc 4444 states
4.5.7.5 READBACK OF CLEARANCES
4.5.7.5.1 The flight crew shall read back to the air traffic controller safety-related parts of ATC clearances and
instructions which are transmitted by voice. The following items shall always be read back:
a) ATC route clearances;
b) clearances and instructions to enter, land on, take off from, hold short of, cross, taxi and backtrack on any
runway; and
c) runway-in-use, altimeter settings, SSR codes, level instructions, heading and speed instructions and, whether
issued by the controller or contained in automatic terminal information service (ATIS) broadcasts, transition
levels.
I would interpret
Level Instructions to include any rate of change given, and as an ATC if this was not readback I'd probably restate
Confirm you copy the rate 1500ft or more or something similar.
ICAO Doc 9432 does not state with a specific rate but does use the term
Expedite
ATC: FASTAIR 345 CLIMB TO FL 240 EXPEDITE
UNTIL PASSING FL 180
Pilot Readback CLIMBING TO FL 240 EXPEDITING UNTIL PASSING FL 180 FASTAIR 345
or
UNABLE TO EXPEDITE FASTAIR 345
So if you substitute
Expedite for the given rate then you would be required to read that back as you would be required to readback the expedite part - at least in my opinion as an ATC its what I'd expect