Means to get the daughter into tennis-playing (7)
I believe the answer is:
intends
'means' is the definition.
('intend' can be a synonym of 'mean')
'the daughter into tennis-playing' is the wordplay.
'the daughter' becomes 'd' (genealogical abbreviation).
'into' indicates putting letters inside.
'playing' indicates an anagram.
'tennis' is an anagram of 'intens'.
'd' placed into 'intens' is 'INTENDS'.
'to get' acts as a link.
(Other definitions for intends that I've seen before include "Aims" , "Has as a purpose" , "Plans, means" .)