Swell up, seeing daughter first to finish (7)
I believe the answer is:
distend
'swell up' is the definition.
('distend' can be a synonym of 'swell up')
'daughter first to finish' is the wordplay.
'daughter' becomes 'd'.
'first' becomes 'ist'.
'to finish' becomes 'end' ('end' can be a synonym of 'finish').
'd'+'ist'+'end'='DISTEND'
'seeing' is the link.
(Other definitions for distend that I've seen before include "Fill out" , "Increase" , "balloon" , "Stretch" , "Exaggerate" .)