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')
'daughter is into tennis-playing' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'is into' indicates putting letters inside.
'playing' indicates an anagram.
'tennis' anagrammed gives 'intens'.
'd' going within 'intens' is 'INTENDS'.
'the' acts as a link.
(Other definitions for intends that I've seen before include "Has as a purpose" , "Plans, means" , "Aims" .)