Hyacinth, say, crossing posh street with vigour (7)
I believe the answer is:
lustily
'hyacinth say crossing posh street with vigour' is the definition.
I can't tell whether this defines the answer.
'crossing posh street with vigour' is the wordplay.
'crossing' is an insertion indicator (to cross can mean to go over or around).
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-u).
'street' becomes 'st'.
'with vigour' becomes 'lily' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'u'+'st'='ust'
'ust' going inside 'lily' is 'LUSTILY'.
Can you help me to learn more?
(Other definitions for lustily that I've seen before include "Vigorously, strongly" , "at the top of her voice?" , "With all one's might" , "In a vigorous way" .)