New arrival carefully selected — 'doubtful breeding', say British involved (8,4)

'new arrival carefully selected' is the definition.
(baby whose genes have been carefully selected)

'doubtful breeding say british involved' is the wordplay.
'doubtful' indicates an anagram.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'involved' indicates putting letters inside.
'breeding'+'say'='breedingsay'
'breedingsay' anagrammed gives 'designerbay'.
'designerbay' going around 'b' is 'DESIGNER BABY'.