Learned to be adamant about closing time (5)
I believe the answer is:
heard
'learned' is the definition.
('hear' can be a synonym of 'learn')
'adamant about closing time' is the wordplay.
'adamant' becomes 'hard' (I've seen this in another clue).
'about' indicates putting letters inside.
'closing time' becomes 'e' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'hard' placed around 'e' is 'HEARD'.
'to be' acts as a link.
Can you help me to learn more?
(Other definitions for heard that I've seen before include "Gathered" , "Tried" , "Detected aurally" , "Got to know (of)" , "Traditional children shouldn't be" .)