Lively agent grabbing a bit of sleep (6)
I believe the answer is:
snappy
'lively' is the definition.
(synonyms)
'agent grabbing a bit of sleep' is the wordplay.
'agent' becomes 'spy' (spy is a kind of agent).
'grabbing' means one lot of letters goes inside another.
'a bit of sleep' becomes 'nap' (I can't explain this - if you can you should give a lot more credence to this answer).
'spy' going around 'nap' is 'SNAPPY'.
Can you help me to learn more?
(Other definitions for snappy that I've seen before include "Irritably abrupt" , "Bad-tempered" , "Quick and energetic" , "without hesitation" , "Cleverly concise; stylish" .)
