Record by one about to show sound reasoning (5)
I believe the answer is:
logic
'sound reasoning' is the definition.
(I've seen this in another clue)
'record by one about to' is the wordplay.
'record' becomes 'log' (logging is a kind of recording).
'by' says to put letters next to each other.
'one about to' becomes 'ic' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'log'+'ic'='LOGIC'
'show' is the link.
Can you help me to learn more?
(Other definitions for logic that I've seen before include "Reasoned argument" , "System of reasoning" , "The science of reasoning from cause to effect" , "method of reasoning" , "Good reason" .)