Speech problem keeps one in care of a parent (7)
I believe the answer is:
aphasia
'speech problem' is the definition.
(aphasia is inability to produce speech)
'keeps one in care of a parent' is the wordplay.
'keeps' becomes 'has' (keep can mean to have or possess).
'one' becomes 'i' (Roman numeral).
'in care of' indicates putting letters inside.
'parent' becomes 'pa' (pa can mean dad or father).
'has'+'i'='hasi'
'a'+'pa'='apa'
'hasi' going within 'apa' is 'APHASIA'.
(Other definitions for aphasia that I've seen before include "Difficulty in communication" , "Trouble getting things across" , "Inability with language due to brain damage" , "Loss of ability to speak following brain damage" , "disorder" .)