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' is the link.
(Other definitions for intends that I've seen before include "Has as a purpose" , "Plans, means" , "Aims" .)