We p-picked up some information – rest may be this (4-6)
I believe the answer is:
well-earned
'some information rest may be this' is the definition.
The definition suggests a singular noun but the answer is not.
'we p-picked up' is the wordplay.
'p-picked up' becomes 'l-learned' ('learned' said with a stammer like 'picked up' was; 'learn' can be a synonym of 'pick up').
'we'+'llearned'='WELL-EARNED'
Can you help me to learn more?
(Other definitions for well-earned that I've seen before include "Thoroughly deserved" , "Justified" .)