Means the daughter is into tennis-playing (7)
I believe the answer is:
intends
'means' is the definition.
('intend' can be a synonym of 'mean')
'the daughter is into tennis-playing' is the wordplay.
'the daughter' becomes 'd'.
'is into' indicates putting letters inside.
'playing' indicates anagramming the letters.
'tennis' with letters rearranged gives 'intens'.
'd' inserted within 'intens' is 'INTENDS'.
(Other definitions for intends that I've seen before include "Has as a purpose" , "Plans, means" , "Aims" .)