"先生のご感想をお聞かせ下さい" means "Please let me hear your(teacher's) impression" The polite form of "聞く" is "お聞き+する"。"お聞かせ+する" is a polite form of "聞かせる(let someone hear)" And "お聞かせ+ください" is a polite form of "聞かせてください(please let me hear)" "聞かせる" is a verb. But we can't add お before a verb, so we change the verb into noun-form "聞かせ". "お聞かせ" is a noun form of a verb. This form doesn't conjugate any more. You can't say "お聞かせる" nor "お聞かせてください". You can just put "する", "ください", "願います" etc.