More polished bone and ivory initiated by queen (7)

'more polished' is the definition.
('shiny' can be similar in meaning to 'polished')

'bone and ivory initiated by queen' is the wordplay.
'bone' becomes 'shin' (shin is a kind of bone).
'and' means one lot of letters go next to another.
'initiated' indicates taking the first letters.
'by' means one lot of letters go next to another.
'queen' becomes 'ER' (short for Elizabeth Regina ie Queen Elizabeth).
The first letter of 'ivory' is 'i'.
'shin'+'i'+'er'='SHINIER'