Beam following quiet request (4)
I believe the answer is:
pray
'request' is the definition.
(I know that plead is the is a more specific form of the action of pray.)
'beam following quiet' is the wordplay.
'beam' becomes 'ray' (synonyms).
'following' says to put letters next to each other.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'ray' after 'p' is 'PRAY'.
(Other definitions for pray that I've seen before include "Offer supplication" , "Call upon in supplication" , "Make supplication (to a god)" , "Appeal to higher authority" , "Beg" .)