Kept going first, in date order (10)
I believe the answer is:
maintained
'kept' is the definition.
('maintain' can be a synonym of 'keep')
'going first in date order' is the wordplay.
'going first' becomes 'main' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'order' indicates an anagram.
'in'+'date'='indate'
'indate' is an anagram of 'tained'.
'main'+'tained'='MAINTAINED'
Can you help me to learn more?
(Other definitions for maintained that I've seen before include "being kept going" , "Declared; supported" , "Insisted" , "Kept up (level)" , "Sustained" .)