Daughter enters wearing uniform -- that comes with stick and carrot! (10)

'carrot' is the definition.
(thesaurus)

'daughter enters wearing uniform that comes with stick' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'enters' means one lot of letters goes inside another.
'wearing uniform' becomes 'inu' (I am not sure about this - if you are sure you should believe this answer much more).
'that comes with' means one lot of letters go next to another.
'stick' becomes 'cement' (to cement something is to stick or attach it).
'd' put inside 'inu' is 'indu'.
'indu'+'cement'='INDUCEMENT'

'and' acts as a link.

Can you help me to learn more?