Sense record must be on since dropping odds (5)
I believe the answer is:
logic
'sense' is the definition.
(logic is a kind of sense)
'record must be on since dropping odds' is the wordplay.
'record' becomes 'log' (logging is a kind of recording).
'must be on' says to put letters next to each other.
'dropping odds' indicates alternate letters (the odd-numbered letters are removed).
The alternating letters of 'since' are 'ic'.
'log'+'ic'='LOGIC'
(Other definitions for logic that I've seen before include "Science of correct reasoning" , "Strict reasoning" , "The science of reasoning from cause to effect" , "Dialectics" , "using premises" .)