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' means one lot of letters goes inside another.
'playing' indicates an anagram.
'tennis' with letters rearranged gives 'intens'.
'd' placed inside 'intens' is 'INTENDS'.
'to get' is the link.
(Other definitions for intends that I've seen before include "Aims" , "Has as a purpose" , "Plans, means" .)