Drink like the cat or the French dog (3,2)
I believe the answer is:
lap up
'drink' is the definition.
(lapping up is a kind of drinking)
'the cat or the french dog' is the wordplay.
I cannot quite understand how this works, but
'dog' could be 'pup' (I've seen this in other clues) and 'pup' is found in the answer.
'the french' could be 'la' ('the' in French) and 'la' is found in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'like' is the link.
Can you help me to learn more?
(Other definitions for lap up that I've seen before include "Scoop" , "Accept with obvious pleasure" , "Eagerly enjoy" , "Drink (water) like a dog" , "of future monarch?" .)