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' is an anagram indicator.
'one' becomes 'i' (Roman numeral).
'inside' is an insertion indicator.
'strong' anagrammed gives 'storng'.
'storng' enclosing 'i' is 'STORING'.
'the' is the link.
(Other definitions for storing that I've seen before include "Putting aside" , "Stashing away" , "hoarding" .)