Keeping the strong obstreperous one inside (7)
I believe the answer is:
storing
'keeping' is the definition.
(storing is a kind of keeping)
'the strong obstreperous one inside' is the wordplay.
'obstreperous' indicates anagramming the letters.
'one' becomes 'i' (Roman numeral).
'inside' indicates putting letters inside.
'strong' is an anagram of 'storng'.
'storng' going around 'i' is 'STORING'.
(Other definitions for storing that I've seen before include "Putting aside" , "Stashing away" , "hoarding" .)