Dine out after start of play -— one of fifteen occupying a certain table (8)

'one of fifteen occupying a certain table' is the definition.
(the actinides are on the periodic table)

'dine out after start of play' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'after' says to put letters next to each other.
'start of play' becomes 'act i' (Act I).
'dine' anagrammed gives 'nide'.
'nide' after 'acti' is 'ACTINIDE'.