Close second, second short on time (6)
I believe the answer is:
strict
'close second second short on time' is the definition.
'strict' can be an answer for 'close' (thesaurus). I am not sure about the 'second second short on time' bit.
'close second second short on time' is the wordplay.
'close' becomes 'r' (I am not sure about this - if you are sure you should believe this answer much more).
'second' becomes 's' (common abbreviation).
'second short' becomes 'tic' (tic or tick can mean a short amount of time; 'short' indicates an abbreviation).
'on' is an insertion indicator (as in clothing 'on' a person).
'time' becomes 't' (abbreviation).
's'+'tic'='stic'
'r' inserted within 'stic' is 'stric'.
'stric'+'t'='STRICT'
Can you help me to learn more?
(Other definitions for strict that I've seen before include "No-nonsense" , "Severe, stern" , "Rigidly enforced" , "Requiring complete obedience" , "Rigorous, severe" .)