Increase favouring prisoner with a case of these (11)
I believe the answer is:
proliferate
'increase' is the definition.
(thesaurus)
'favouring prisoner with a case of these' is the wordplay.
'favouring' becomes 'pro' (I've seen this in other clues).
'prisoner' becomes 'lifer' (lifer is a kind of prisoner**).
'with' means one lot of letters go next to another.
'case of' says to hollow out the word (remove centre letters) (outsides of).
'these' with its middle removed is 'te'.
'pro'+'lifer'+'a'+'te'='PROLIFERATE'
(Other definitions for proliferate that I've seen before include "Mushroom" , "Reproduce rapidly" , "Increase rapidly in number" , "spread" , "Grow rapidly in number" .)