Beak retaining old form of capital punishment (5)
I believe the answer is:
noose
'form of capital punishment' is the definition.
(a noose is used to hang someone)
'beak retaining old' is the wordplay.
'beak' becomes 'nose' (I've seen this before).
'retaining' indicates putting letters inside.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'nose' going around 'o' is 'NOOSE'.
(Other definitions for noose that I've seen before include "Cord snare" , "Sliding loop in a lasso (5)" , "Loop with running knot" , "marriage, for a laugh" , "Loop in a rope made with a slip knot" .)