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19d "something valuable in one's house"(6) I have *e***i - I'm sure of these two letters, but am scratching head !
26a "Italian with alluring air oddly rejected"(5) - I'm thinking Latin but don't know why - the third letter of this clue gives the fourth on the one above
20d "Police leader once detaining first of race horses"(6) - *t***g - ?String? - but why ?

Police = the pop group, leader STING

20d refers to the band Police, led by Sting - first of Races inside

Gem in i - horoscope house?

1d long shot (no explanation) - MEDICI?

Luigi? (letters are oddly rejected?)

Thanks, all. I am grandfather to twins, so really ought to have got Gemini !!