Smarter daughter limits team leader's part of vessel (8)
I believe the answer is:
potsherd
'part of vessel' is the definition.
(piece of a ceramic vessel)
'smarter daughter limits team leader's' is the wordplay.
'smarter' becomes 'posher' (posh can mean smart or fancy).
'daughter' becomes 'd' (genealogical abbreviation).
'limits' indicates putting letters inside (limit can mean to contain or block off).
'leader's' suggests taking the first letters (I've seen 'leader' mean this).
The first letter of 'team' is 't'.
'posher'+'d'='posherd'
'posherd' placed around 't' is 'POTSHERD'.
(Other definitions for potsherd that I've seen before include "Broken piece of ceramic" , "Piece once fired" , "A broken piece of earthenware in archeology" , "Pottery fragment; the drops (anag.)" , "part of vessel found in digs" .)