Branch in the morning admits first of regulars
I believe the answer is:
arm
'branch' is the definition.
(synonyms)
'morning admits first of regulars' is the wordplay.
'morning' becomes 'am'.
'admits' indicates putting letters inside.
'first of regulars' becomes 'r' (1st letter of 'regulars').
'am' going around 'r' is 'ARM'.
'in the' acts as a link.
(Other definitions for arm that I've seen before include "Body part" , "Limb or branch" , "Test of strength with elbows on the table" , "Provide with weapons" , "One fired" .)