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