Quickly suggest reduced hydrogen in sample (4-5)
I believe the answer is:
post-haste
'quickly' is the definition.
(to do something post-haste is to do it quickly)
'suggest reduced hydrogen in sample' is the wordplay.
'suggest' becomes 'pose'.
'reduced' means to remove the last letter.
'hydrogen' becomes 'H' (H is the chemical symbol for hydrogen).
'in' is an insertion indicator.
'sample' becomes 'taste' (synonyms).
'pose' with its final letter removed is 'pos'.
'h' inserted inside 'taste' is 'thaste'.
'pos'+'thaste'='POST-HASTE'
(Other definitions for post-haste that I've seen before include "without delay" , "With utmost speed - to the pass (anag)" .)