Pressingly, yet quite slowly for half an hour (8)
I believe the answer is:
urgently
'pressingly' is the definition.
(I've seen this before)
'quite slowly for half an hour' is the wordplay.
'quite slowly' becomes 'gently' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'for' is a charade indicator (letters next to each other) (I've seen this in other clues).
'half an' means to take half the letters.
'hour' halved is 'ur'.
'gently' after 'ur' is 'URGENTLY'.
'yet' is the link.
Can you help me to learn more?
(Other definitions for urgently that I've seen before include "Immediately, with pressing need" , "Pressingly" , "without delay" , "Earnestly and insistently" , "with expedition" .)