Improve cries of derision on time (5)

I believe the answer is:
boost
'improve' is the definition.
(thesaurus)
'cries of derision on time' is the wordplay.
'cries of derision' becomes 'boos' (I can't justify this - if you can you should believe this answer much more).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'time' becomes 't' (abbreviation).
'boos'+'t'='BOOST'
Can you help me to learn more?
(Other definitions for boost that I've seen before include "Push upwards, help" , "Increase (strength or morale)" , "Give more impetus to" , "Fillip" , "Recharge" .)
