Continue to behave strangely (5,2)
I believe the answer is:
carry on
'continue' is the definition.
(carry on can mean to continue or keep going)
'behave strangely' is the wordplay.
'behave' becomes 'carry' (synonyms).
'strangely' becomes 'on' (I can't justify this - if you can you should give a lot more credence to this answer).
'carry'+'on'='CARRY-ON'
'to' is the link.
Can you help me to learn more?
(Other definitions for carry on that I've seen before include "Flirt" , "Continue like English series of risque films" , "Have an affair - cause a fuss - continue" , "hand luggage on American Airlines?" , "Continue like British comedy films?" .)