6a Subject this person to anti-discriminatory checks (5)
Must be topic = subject, can't parse it though.
10a English teacher's back in a panic, providing cover for head (7)
Earflap? E = English, flap = panic, but how does ‘ra’ mean teacher or teacher’s back? And do earflaps cover the head anyway?
8d Bard's trick, capturing a Trojan lover (9)
Caparison? If so, how does this mean bard? I can only find it meaning a sort of cloak for horse.