It'll go up after a while (4,4)
I believe the answer is:
time bomb
'it'll' is the definition.
I can't judge whether this definition defines the answer.
'up after a while' is the wordplay.
'up' becomes 'bomb' (I can't justify this - if you can you should give a lot more credence to this answer).
'after' means one lot of letters go next to another.
'a while' becomes 'time' (I've seen this before).
'bomb' after 'time' is 'TIME-BOMB'.
'go' is the link.
Can you help me to learn more?
(Other definitions for time bomb that I've seen before include "Exploding ticker?" , "one could go off after a while" , "Thing set to explode" , "Device set to explode later" , "Preset explosive device" .)