Son darts around quietly delivering fliers (8)
I believe the answer is:
sparrows
'fliers' is the definition.
(sparrow is a kind of bird)
'son darts around quietly' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'darts' becomes 'arrows' (I've seen this before).
'around' is an insertion indicator.
'quietly' becomes 'p' (p for piano and quiet).
's'+'arrows'='sarrows'
'sarrows' enclosing 'p' is 'SPARROWS'.
'delivering' is the link.
(Other definitions for sparrows that I've seen before include "Small brown birds" , "Small singing birds" , "These birds warp Ross badly" .)