Modest about myself and daughter in drama (6)
I believe the answer is:
comedy
'drama' is the definition.
(comedy is a kind of drama)
'modest about myself and daughter' is the wordplay.
'modest' becomes 'coy' (I've seen this before).
'about' indicates putting letters inside.
'myself' becomes 'me'.
'and' is a charade indicator (letters next to each other).
'daughter' becomes 'd'.
'me'+'d'='med'
'coy' going around 'med' is 'COMEDY'.
'in' is the link.
(Other definitions for comedy that I've seen before include "Play or film designed to evoke laughter" , "Dante's divine work" , "Light amusing performance" , "film like Doctor in the House" , "Funny and/or happy play" .)